Using RDP as a verb?

This is, of course, not standard English. My convention, which plays nicely with old fashioned WikiWiki sites, is to use apostrophes when conjugating, and treat 'to RDP' as the infinitive of a regular verb (in general). First, I shall go through these replacing RDP with 'wink'. We get:

1. I winked to the server
2. I wink to the server
3. You should wink to the server
4. I was winking to the server
5. I was wink to the server

Clearly 5 is wrong. For the other four (and to make it clear that the suffix is grammatical, and not part of the original abbreviation), consider:

1. I RDP'ed to the server
2. I RDP to the server
3. You should RDP to the server
4. I was RDP'ing to the server

In precise correct English, RDP is not a verb, and cannot be used in the manner you quote. If you are writing formal English you should avoid it. "I used RDP to connect to the server" would be a correct formal sentence.

However informally and in technical writing, use of nouns as verbs is very common. (As I heard it: "These days any noun can be verbed.").

If you do use this, or in any other case where a noun, noun-phrase or acronym is substituting for a verb, consider the basic form of the noun to be the present tense, and follow the usual rules of tense and modification.

Of the five sentences you write, there's nothing explicitly wrong with any of the first four, as they would be correct for any other regular verb (remembering that this is informal English). The fifth is wrong, as you would not use the present tense following 'was'.

I have seen the construct "I RDP'd to the server', but the use of apostrophe d to mean past tense hasn't been common in English for over a hundred years, and is now found mostly in old hymn lyrics.