I only really have the expertise to answer your questions on marriage, so will leave the other questions to those best equipped to answer.

How much choice women had in marriage varied greatly depending on their social status and their family. Some parents (there's circumstantial evidence that women were as involved in organising marriages as men) took their children's desires into consideration more than others. Evidence from my research suggests that marriages were often arranged in order to facilitate a positive relationship between the couple: husband and wife were near the same age, would have met previously, etc. But equally, there were times when the necessity for a marriage was so great (to prevent a war or to acquire a particularly juicy piece of land) that it might be arranged with little regard for either party's happiness.

At the highest levels of medieval society, most women would have known from childhood that marriage was their destiny. Princesses were primarily used in international diplomatic marriages and were very valuable in this regard, so most did marry. Marrying a large number of daughters could be a challenge, though, so if you had a lot of older sisters, there could be more flexibility for you. This would almost certainly mean entering religious life.

If your father picked out a husband for you and you really, really didn't want to marry him, there were options open. First, medieval canon law clearly stated that a marriage could only be formed by the freely given consent of the couple involved. This was formalised in the early thirteenth century, so your 11th-century princess had autonomy, but a couple of hundred years later, she would be good. If you absolutely refused, you could not legally be married. We have no way of knowing how often this happened, but it seems to have been very rare. Families could put a great deal of pressure on their daughters to marry according to plan (the marriage of Jane Grey to Guildford Dudley in the 16th century is a classic example) and everyone would have been raised with the idea of arranged marriages as the norm.

Another option was to find someone else to marry in secret. In 1297, Joan of Acre, the widowed daughter of Edward I, secretly married her esquire, Ralph de Monthermer. Joan, who was only 25 and had had children, was a valuable commodity on the marriage market. Her decision to marry in secret instead of keeping herself available for a diplomatic marriage angered her father. Joan was far from the only widow to employ this tactic: Alice de Lacy did the same when she married Ebulo Lestrange in 1324; Catherine de Valois married Owen Tudor at some point in the 1430s; Jacquetta of Luxembourg married Richard Woodville in 1437. A woman who wished to remove herself from the marriage market had the ability to do so, but it's interesting to note that each of these women did so as a widow. My own research backs this up -- younger women on their first marriage were more likely to follow the wishes of others, but widows likely had a bit more leeway flout expectations.

As mentioned above, if you did marry, your husband would likely be an important foreign prince or nobleman. Who exactly he would be depended very much on which way the political winds were blowing. Is there worry about war breaking out with France? You're marrying a French prince! Has war broken out? You're going to marry into the family of one of France's enemies in hopes of making any alliance. Is your country looking to expand trading relations somewhere? That's where your husband will probably come from. This wasn't always a given. Princesses did marry men from their own countries, particularly when relations between the crown and the nobility were tense. In the late 13th century, Edward I developed a policy of marrying his daughters to important English earls, in order to more closely align the interests of the crown and the top tier of the nobility.

If your husband or fiance died, you would often (though not always) be expected to make another diplomatic marriage. As in the case of Joan of Acre, women who were still young remained valuable on the marriage market, especially if they had already demonstrated their fertility by having children. There might be other ties that forced (or allowed, depending on your perspective) you to remain single. If you had a young son who had just inherited the throne, you might remain single in order to exercise on his behalf. If you were older, you might not remarry and either return to your home country or remain in your husband's country. Such women would have a bit more choice over whether to enter religious life or stay in lay society.

If you hadn't married yet and your fiance died, your father (or whoever was planning marriages for you) would likely re-open marriage negotiations elsewhere pretty much immediately. This was a very common occurrence. Betrothals could fall apart for a number of reasons and many women were betrothed multiple times before marrying.