Answering a question like this requires a couple of clarifications about the nature of the Imperial economy, and especially its form after 1648: a framework for understanding the data presented below. All throughout the Empire's history, attempts to tax the princes of the Empire on a regular basis, or any one that we might understand as "tax" in a modern sense really, were mostly ineffective, due in large part to the fact that the Emperor could get individual princes to fund their contingents in his armies simply by not paying them - they were still feudally obliged to serve him.

Although the Salians attempted general-tax projects on a few occasions during the later 11th Century and early 12th Century, as did Frederick II in 1241. It didn't help that the Salians made their attempts in the midst of civil wars! Nevertheless, this was not an area of particular concern for Emperors solely because the feudal reforms of 1230 ensured the participation of vassals in military conflict; other than that, the Emperor would be expected to fund his own court, and there were few other areas of Imperial state to furnish with money in the first place.

However, by the 15th Century, problems with this very loose policy of taxation began to rear their heads as the cost of war rose and disparately situated and culturally differentiated princes often found it easy to shirk their duties. Therefore, a couple of general taxes were called, notably and first in 1422 over the Hussite problem. However, reform only properly came through in 1495, when the "Common Penny" tax was introduced to the Empire, raising much more money than previous taxes were able to with its stronger legislative framework.

Nevertheless, the lack of an Imperial army distinct from the individual - or individually funded - princes' armies (and, of course, that of the Emperor - or more accurately for the period you are talking about, the Austrian army) meant that only a small bureaucracy was needed; the Reichskammergericht (Imperial Cameral Court) and Reichshofrat (Imperial Aulic Council) and other Imperial bodies were small in comparison to their counterparts in the rest of Europe. This is not to say that they were weak, of course, but that there was simply less necessity for a massive state apparatus.

In answer to your first sub-question, the coffers of the Empire were seperate from those of Austria. At least in name, though actual exercise of this power was infrequent, the Elector princes chose the new Emperor every time the old one died; therefore, even though there was only a three-year period outside of (normally Austrian) Hapsburg rule between 1438 and the dissolution of the Empire in 1806, the legal and formal separation between the Empire and Austria needed to be concrete in order to avoid a loss of favour from the Electors and, in extremity, actual loss of Hapsburg power.

Moving on to the surprisingly brief main body of the question, however, the Imperial budget itself was, as noted above, primarily to do with military matters, with a few supplementary legal and bureaucratic elements added on top to ensure the coherent functioning of the Empire. Although, after the weakening of Imperial authority crystallised in the treaties of 1648, collection of taxes for war was on an ad-hoc basis - usually in the form of "Roman Months", a set amount of troops to be supplied to the Emperor, or their worth in money, or around 50,000 florins by the 18th Century - but nevertheless extant.

Around 1780, for example, the total amount of revenue derived from Imperial prerogatives was 103,484 florins. Meanwhile, the annual tax introduced in 1507, the Zieler, was meant to be about 120,000 florins per annum by 1720, 25% more than what was necessary for wages of bureaucrats and legal staff; in practice, the amount of money gathered up by the Imperial apparatus ranged from 78,000 to 139,500 florins between 1742 and 1770. This meant that, in some years, there was not quite enough money coming in, and in others, enough to make up the deficit. Those, however, made up the main two streams of peacetime income for the Empire together.

This shows us a couple of things overall. The Imperial budget, in times of peace, came to somewhere around 200,000 florins annually, to cover the maintenance of military forces and the state apparatus of the Empire. The significant variances in actual amounts of money recieved by the Emperor are demonstrative of the decentralised, or devolved, nature of Imperial government, but they do not show that it was weak at all. It was in fact quite efficient, allowing minor legal disputes to be dealt with locally, saving its comparatively sparse peacetime funds for high courts. Of course, this still caused problems, but that is for another time! I hope this helped, and thank you for the interesting question!

​

Sources:

Musgrave, The Early Modern European Economy

Whaley, Germany and the Holy Roman Empire 1493-1806 [Volume II]

Wilson, The Holy Roman Empire