1) In general, using a higher voltage rated replacement capacitor is a good idea (i.e. using a 50V instead of the original 35V capacitor)... provided that variations in physical package size (and possibly cost) do not create an issue.
Apparently there is a threshold where an increased voltage rating may not be a good thing. Electros are supposed to operate at some minimal percentage of their rating in order to keep character of the capacitor's construction. I am not going to cite the preferred %, in case I have not remembered it correctly. Jumping from 25 to 35 Volts would be well within the green zone.
2) Whenever possible use a replacement cap rated for higher ambient operating temperatures... i.e. 105C instead of 85C.
Provisionally, I would say 'yes', but as long as all the other specifics were coinciding with your needs. Of course, if the capacitor is especially subject to heat, as indeed they often are — especially in power supplies and tube gear — the higher rating would probably have priority over everything else.
3) Lower ESR is always better
If we really know what we are doing, I think that each cap would be chosen precisely for its specified characteristics. Get any comprehensive catalogue of electrolytics and notice how each manufacturer has a wide range of products. The relevant charts often have headings that illustrate the feature each series offers, such as long life, low DC leakage, low ESR, high ripple current, specifics for dielectric absorption etc. Sometimes these features are juggled to create smaller sizes and so on. Some series are undoubtedly attempts to combine as many of these desirable features as possible in one package. ‘General usage’ denotes the obvious. Price is an issue.
In order to make the best and most efficient choices, we would be very knowledgeable about the circuits we are working on. We might choose exactly the right capacitor for each location in the circuit. This possibility excludes me, because I am too inept at understanding circuits. My solution is to choose caps that roughly meet the more obvious demands. In digital circuits I want stability and low ESR. In power supplies I want low leakage, high ripple current, long life and often a high temp rating. Like that ....
4) Generally speaking, all replacement caps must have the same capacitance value as the original.
This is one of those old saws :deadhorse Some writers say that the original designers were not dumb, and the bulk costs of caps to manufactures is not the determining factor to the extent that performance is compromised for want of L. Still others seem to recommend beefing up power supplies and other sections as a matter of course. I take the weasel approach. I assume that the original design is adequate unless it is a famous fact known far and wide that it isn't. Then I try to find the best cap that I want to afford and will fit the space. For my needs, all the above stuff in #3 gets considered along with the fact that physical size (i.e. larger) is preferred. I am too ignorant to beef up values in some hope that it is better. There are some cases when it definitely isn't. It is easy to create stresses downstream unless you really understand your circuit.
That is as much as I can say without being flamed for being a moron. But I believe that everything I have said applies to common sense for the novice as it is informed by some 'basics'. For the more adept, modifying and altering circuits is part of the fascination of this hobby, mania or passion.