There’s an awful lot of questions buried in @Makronax_Solarius’s post. But since it’s all Amarrian focused that’s like catnip to me…
All the four Empires have good mission running ships. The main distinction is personal preference. They have different advantages and disadvantages.
For example, the Amarrian Apocalypse has a bonus to tracking (to hit small targets harder) and range (which equates to damage as you can use more powerful crystals) but is locked to EM/Thermal damage types.
A missile ship or drone ship may be able to change damage types, but they have time to impact or other issues that mitigate that advantage.
It really is preference. If some one says “X is best” what they really mean is “X matches what I want and how I fly”. @Oriki_Ahvilen has covered that well above.
I fly a Harbinger for Level 3 missions and an Apocalypse for Level 4. The Maller or Omen is fine for Level 2 - though I prefer the Omen.
Amarr does have drone boats, many almost on par with their Gallentean equivalents, but with bonuses to support systems. The Vexor and the Arbitrator both have a 10% per level bonus to drone hit points, but the Arbitrator has an e-war bonus as well rather than a second weapon bonus.
The Arbitrator is a reasonable mission ship and a cracking fleet support ship, tracking disruption, DPS or ECM drones. Good days.
The Capsuleer alliances and corporations are independent of the NPC empires/factions. However there are groupings that for RP (role playing)purposes align themselves with the Empires. I know the Amarrian loyalists best: SFRIM/LUMEN (“The Society”), CVA - The Paladin Wardens, and PIE (“The Praetoria”), but others exist aligned to the other factions.
There is RP interaction between CCP and these groups. And that includes ongoing storylines and events. Yeah, being a Chapter in the Empire has consequences. And a nice title.
Which means Question 3 is: by talking to people.
I’m happy to make introductions.
Most groups will have an area they call home, for some that’s in high security space, for some that’s particular bits of null security space they have managed to carve out for themselves. But many alliances often cover all security aspects. Perversely it’s sometimes the bigger high sec groups that cover a wider range of security space since they will roam or visit into low and null, where as some of the null blocks rarely visit high sec except with out of alliance trading alts.
You do get big conflicts and battles in high-sec. They don’t get the publicity of the Trillion ISK fights in null - the very expensive capital fleets can’t get involved, so combat is in sub-caps: battleships and smaller, but action is there. I fought at Thebeka a large RP driven conflict that was a lot of skirmishing ending in the forcible removal of the opponent. High-sec war mechanics make for a different type of conflict as forces manoeuvre and alliances have to formally declare war.
Take your time, you don’t have to settle in the first place with the first group you find. You want somewhere that meets your wants and needs in New Eden and finding that can take time. “You have to join a Corp” is the same as “you must fly ship X”. An opinion, not a rule.
Oh, and most importantly:
Welcome to Eve.
Welcome to life in New Eden.
Jump on in: the water’s lovely.