If i understand, you can roll for psionic strength whenever you want...but why would not all characters roll before the first career? And would that mean that most people in the Traveller universe (at least pc material) are psi competent? That seems a little too much...i must be missing something.
As noted, it depends on the GM. In theory, however, you should only roll when specifically told to - i.e. you enter a psion career, or roll a "you're psionic!" event, or with the GM's permission if you've agreed you're going to try a psion career.
In settings where psionics are uncommon or illegal, he must find a teacher, normally one of the underground Psionics Institutes. Finding such an instructor is an adventure in itself.
I.e. something you shouldn't just be able to declare "I did that" during character generation without some level of discussion.
Is the only limiting factor the 100,000 credits it costs to get trained? Otherwise, according to the corebook rules, pretty much anyone would have a psi score around 7, which is quite decent.
If you're going to allow people to roll at character creation, then yes. Normally, though, people only roll the relevant life event some time into their career, when that penalty-per-term will keep them down to a lower level, if they ever roll it at all.
And if a pc decides to test for one of the psychic careers, do he need to pay the 100,000 credits to be trained?
And can a pc raise his psychic skills like any other ones?
In theory, I guess. They are skills, after all.
Lots of questions...i just find the psychic rules a little unclear. In addition, psychic powers seem to be very powerful.
It's deliberately so. Psychic skills aren't a 'spell' so much as a skill. By which I mean that rather than 'throw a fireball with range X, damage Y and Psi cost Z', pyromancy-type abilities are 'you can remotely apply heat to something. You figure out how best to use this.'
They both are and aren't powerful.
Teleportation is a good example - you can get literally anywhere, instantly, bypassing perimiter defences, doors and guards, provided you don't mind arriving as a hypothermic naked guy. Which kind of limits your ability to achieve much when you do.... :?
Telepathic assaults are awesome in theory, but you have Telepathy and Assail and I'll have Gun Combat (Slug Rifles) and an ACR and we'll see who wins. Telepathic interrogation is in theory very effective but no better than the scientific application of stabby things and burny stuff.
Awareness is probably the best single talent because all it does is make you better at what you're already good at.
Is there an advantage/reason for not checking for all PSI talent acquisitions first, in hopes of getting PSI talents by rolling on the Service Skills table later during the Psion career?
No. As with skills, if you roll up a skill you don't have, you gain it at level 1. So you can subsequently pick up talents you didn't get to start with.