Historically, producing a child out of wedlock with the hopes of them becoming a feasible heir would be pure insanity, since their claim would be contested by a host of pretenders born in wedlock. It did happen occasionally in medieval monarchies that illegitimate children came to power (William the Conqueror and Henry II of Castille come to mind), but in most cases, this would be the result of a very specific chain of events or state of circumstances, and the fact of being illegitimate always weighed heavily against the candidate's claim.

For example: Alfonso XI of Castile had a legitimate son with his second wife, who was called Pedro, in 1334. Later on, he had a host of illegitimate children with his lover, Leonor de Guzmán, the third of whom was Henry, born in 1333. When Alfonso died, Pedro succeeded him without any major inconvenience, but he quickly acted cruelly against his bastard's brother kin, possibly to preempt any possible move by them against him, as his father, king Alfonso had given them extensive lands and power. Henry, by then count of Trastámara, revolted against Pedro, seeking the help of the king of Aragon and many nobles in Castile who had been wronged in one way or another by Pedro I, known as The Cruel. After and arduous civil war, Henry managed to defeat and personally murder Pedro I, obtaining the throne of Castile and hence installing his dynasty in the kingdom. It's important to note that his victory was VERY hard to achieve, and the fact that Pedro I often alienated his allies through his cruel actions (and pettiness, for example not paying his English allies led by the Black Prince their dues), was key in making Henry's victory possible.

In the same Iberian context, there's another example, in which the illegitimate candidate lost. Martin I of Aragon died without any living son. His closest of kin would have been Fadrique, the son of Martin the Younger (Martin I's son) and an Italian noblewoman: Tarsia Rizzari, so his claim would have been strong, except for the fact that he was a bastard. Instead, a host of other claimants to the Aragonese Crown offered their candidacies, which were all much weaker than his, if it weren't for the fact that he was illegitimate. The whole matter of this succesion was long and incredibly complex, involving all sorts of political considerations, even the schism of the catholic church, but it ended up being resolved by a number of commissioners who gathered in Caspe to analyse all the candidacies and choose whoever they saw as the most fitting: all of them agreed that Fadrique's claim was the weakest.

As for the second question, I'll preface it by clarifying that in the Middle Ages, the lack of an actual consolidated state meant that measures taken by the central government were often scarce, but particularly, they had a different scope from what we might imagine with our modern perspective. Political economy as a field was barely starting to be insinuated, for example in John of Salisbury's (115-c. 1180) Metalogicon and Policraticus, where it was deeply intertwined with political theory, and of course, theology.

So, the modern, centralised vision of economic planification, did not exist back then. Instead, you would have specific measures undertaken to deal with specific problems in a fairly isolated manner, and most importantly, divided locally or regionally depending on the status of the territory in question. Medieval monarchs actually exerted their rule most effectively within their own patrimony (which was never the whole extent of the kingdom), and held much less influence over lands that were under lordly jurisdiction. Their capacities to direct government in such places depended on the specific circumstances of each kingdom, and even each locality. The rights to mint coin, for example, were some of the ones most monarchies had considerable control over, and were usually careful in granting that right to other lords. So specifically financial measures, like altering the amount of precious metal in a given currency, could have been well under the control of the monarch, but even that was often easily done. For instance, in Castile (I've been studying the Iberian kingdoms recently, so that's why I'm talking a lot about them, sorry), the "Cortes", whcih were a parliamentary organism, often granted resources to the monarch in several forms, after getting him to agree not to alter the currencies law (its weight, purity, and proportion of precious metal) for a given time, so as not to cause harm to their trade. This was done so repeatedly that it became customary for the monarch to swear during each summoning of the Cortes, not to alter the currency's law for the next 7 years, obtaining several loans and other benefits from the Cortes in exchange. Other measures that were taken in a centralised form were largely judicial in nature: proclaiming codes of law or confirming those granted previously (most often on a case-by-case basis, pertaining to different localities), or granting "immunities" (delegations of royal jurisdiction on certain vassals, often as part of lordly grants). Things that could be dealt with in these legislation would be for example the right of a city to collect taxes from merchants who brought goods in to sell, the right of a given entity to collect taxes from a bridge, or to have a monopoly over certain services, like a mill, a foundry, an oven (usually large ones and used for artisanship), or even an inn. Another matter that was dealt with centrally was external trade: monarchs could, and often did, give certain legal and/or fiscal privileges to merchants from given places in order to attract their trade.

However, most of the core economic and demographic growth took place on a strictly local level. The period between the late 10th century and the early 14th is fundamentally a period of economic and demographic expansion, fueled in part by technical improvements (better yokes, the increasing use of horses for ploughing instead of oxen, more varied crops, 2 or 3 field crop rotation, better tools, etc.), but more so by a quantitative improvement: sections of forests were cut down to make way for more farms, some swamps were dried out to make the land available, etc., all of which brought about an increased and more varied food supply. This expansion was most often born of some lord's initiative, be it a monastery, a free city, a baron, a count, a duke, whatever. To do this, they needed more people to immigrate and do the actual work needed to achieve this agricultural expansion, and to do that, they generally offered incentives: fiscal exemptions, favourable leases, or even tenancy. An interesting case is the contract signed by the tenant and the farmer of a plot that was intended to produce vines; these specific contracts are abundant in Spain and Italy, and they present wide variations and evolutions, but one of the most common was the one that gave permission to the farmer to work the plot of land until it started production (a long time, about 5 years if I recall correctly), and after that period divided profits roughly equally between the tenant and the farmer.

As for foreign relations, the understanding of war as a continuation of politics or economics is modern, and as such didn't exist in the Middle Ages. It's obvious that monarchs did have such considerations in mind, making strategic alliances and such, but ti was all tainted by a dynastic view of foreign relations, and by concepts of justice and rights. Hence, most declarations of war had relatively valid excuses as casus belli: be it dynastic rights over a certain place, reparations for some wrong done against the aggressor, the defence of a relative's claim, etc. In other cases, highly complex arguments of political philosophy were wielded as motives: for instance in the dispute between the Holy Roman Empire and the Papacy over investitures, and in Henry of Trastámara's war against Pedro I, where his jurists claimed that Pedro I forfeited his right to rule by doing so unfairly, which has been regarded as a loss of "rights of exercise" by historians.

I don't have much time to expand this answer any further, so I hope this will be helpful.