Yes, you can absolutely apply for conference and compute funding, separately from an application for salary, or in combination. E.g. if you're applying for salary funding anyway, it would be very common and normal to also apply for funding for a couple of conferences, equipment that you need, and compute. I think you would probably go for cloud compute, but I haven't thought about it much. 

Sometimes this can give mild tax issues (if you get the grant in one year but only spend the money on the conference in the next year; or, in some countries, if you just receive the funding as a private person and therefore can't subtract expenses).

Some organisations also offer funding via prepaid credit cards, e.g. for compute.


Maybe there are also other options, like getting an affiliation with some place and using their servers for compute, but often this will be hard.