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You cannot increase any given skill beyond its maximum for your current level, which is 10 + 5 per level.
Related base abilities
Each skill is affected by one of your character's Base Ability Scores, but the amount of points you may invest in any skill is not restricted by them. Every point in base ability above 4 increases the effective value of dependent skills by 8.5%, while every point below 4 decreases it by 10%.
Skill synergies
Some skills also benefit from others through skill synergy, increasing their effective skill level by a percentage of the synergistic skill. Synergies cannot boost skills beyond their maximum for your current level.
AND you must understand the concept of effective skills and abilities, see In-depth FAQ, Game mechanic explained part I, Concept of effective skills and abilities
Now let's take a look at a real example, it'll help if you follow along using the build tool[underrail.info.tm]:
At level 1, your maximum base skill is (10 + 5 * level 1 =) 15
Looking at the three psi skills - thought control, psychokinesis, and metathermics you can confirm the maximum base skill for them are indeed 15. Now max them all out using the build tool.
The effective skill maximum depends on a skill's related ability, in this case, WIL, change WIL to 10. At WIL 10, you have 6 ability points above 4. Now you'll see the maximum effective skill is now (100% + 8.5% * 6 = 151%) -> (151% * 15 = 22.65) -> 22. You can change the maximum effective skill for any skill by playing around its related ability.
If you hover your mouse over thought control you'll see "Skill synergies: 10% psychokinesis 10% metathermics". Skill synergy is pretty straight forward - for thought control you'll get an increase in effective skill of 10% from psychokinesis and 10% from metathermics. However the effective skill cannot exceed the maximum, which we just calculated to be 22.
So to answer your original question: At the character creation, every point gained through synergy / attributes past the 15 limit are wasted and give no effect ?
Yes and no as this really depends on your skill point distributions and their related abilities.
My advice to the average player is to ignore the skill synergy bonus for now. If you want to plan out a new build just follow my steps in my In-depth FAQ, Character build part I.
What I wondered was, should I max every skill I want to be good at or should I only read the brackets number to reach the level cap limit and everything higher is a waste that the game didn't tell me.
Your exemples are perfect, I did a psiker and you don't want to loose any points in this game.
This game is soo badly explained / unintuitive, I'm ok with a game making you discover things, like lore, but the principle of a game is that you should be aware of the rules, the mechanics.
I wouldn't worry about level cap limit at all. Synergies bonuses are pretty insignificant - open the build tool, set up a level 25, WIL 16 char, max any two psi skills and you'll see you only get a 26 synergy bonus for the remaining psi skill. For you first psi char I would suggest you max out all three psi skills and test things out. Unless you play something disastrous like a WIL 3 pure psiker the level cap limit and skill synergies aren't a factor at all.
Once you complete a game by beating the final boss you'll have a much better understanding of the game mechanics: some feats are essential for certain chars; how various different psi abilities works and whether a "spell" is good in the field; some control abilities are better than others, and you don't have to max and/or invest much skill points for them to work, etc. Once you grasp the game mechanics you can start messing around and do weird but powerful hybrid build like a metathermics sniper. :)
I think I understand your question now - any effective skill higher than the maximum base skill is not a waste. For example if you have crossbow 135 (238) - yes your max base skill is 135, the 238 effective xbow skill is not a waste above 135. In fact, the damage and accuracy of your xbow is now calculated using only the effective value. The base value is pretty much ignored by the game except to check for feat requirement.
Edit: I think you are confusing max base skill and max effective skill. They are two completely different thing.