So, im new to the game and i have some issues i can use help with:

1:I have surveyed a solar system and i want to build a starbase on it but when i order my construction ship to do so nothing happens, What should i do?

2.I want to colonize one of the planets on the solar system but the game keep telling that i cant do it becuse the planet is not in my borders, How do i get it into my borders? ( i already have survied the system)

3.Its seems like once i survyed the system i already started to receive recorses from the this solar system if so,
what is the purpose of mining stations?

1: Do you have a screenshot?
2: By building a starbase on it.
3: Do you have a screenshot?

1 I would assume you don't have enought to build the base... a sreenshot of your game would tell us

2. you must build a base to claim that system for your side before you can use the planets or mine anything

3. you get nothing until you build the base to claim the system... once you have a small base the trade in that system may auto collect but other things will need you to build their unit i.e, minning base to collect ore etc

here is a screen shot.
i dosent look to me like im lacking in resources but maybe you can see something thati im missing

Edit:i tried to attac the screenshot to the reply but u dont see that anything happen and for somereason i cant post links right now /:

fyi the game takes screenshots in Png and this forum only allows jpeg so you need to convert it first

This is some of my early game trade maps
I have plenty of ore but only 43 influence... I need 52 to build a new base in unclaimed territory because I spend an ascension point to get cheaper bases

I have unclaimed trade in Algorab, Ruthouri and Neetris systems... Neetris has already been surveyed but its a dead end so I won't send my construction ship because at this stage of the game its more important to push my empire boarders out and I can come back to grab it later

Note the shading around the Neetris system tells me it has been explored but my empire stops at Algorab

My base in the Nigiro system has a small amount of 10 trade going to sol Aclr'Roka (capital) and if I ignore this then pirates will build in the Camthrin and Banthelgaum systems so I have a small fleet of 3 ships just patrolling back and forth between those two until later in the game when I will add guns to sol and Nigiro bases... Right now 3 small ships is cheaper

I will add a base to Ruthauri to collect the 3 trade and watch that boarder then I will need at least one more base to get Algorab & Neetris trades which will probably be in the Vlriak system so that one trade platform can get them both

The north trade route from Romston is much bigger and you can see pirates would become a problem in Sirius, Ebbarmacchus and Bamard's star if I didn't also have another fleet of 5 ships patrolling those 3 then I would lose some of that trade and eventually pirate fleets would appear on the map as well

so many stuff i going on in your screenshot, i locate neetris
any way thank for the heads up about the PNG this explains why i couldnt attach it.
here is the screenshot

you need to send a science ship with hero to survey the system... in fact it tells you that in the title under the system name

once your system is fully explored then you can have your construction ship build a base to claim it + you also have reserch not being done so I assume some event took away some of your science heros

this is odd i did sent a ship. maybe she didnt completed the survey. any way thanks!

Sometimes , actually quite often, your scientists will become President by winning the election. You have to pay attention to who wins elections and fill their job with a new person. It could be a researcher, or a science ship officer, in either case progress will stop if the position is not filled. Same goes for Governors, you would have a sector without a leader if a Governor won the election, and you did not choose a new one.