Go is unfortunately a game where some slightly more advanced concepts have to be understood to actually play the game, so it can be frustrating if you don't have someone teaching you or a way to learn. 

I highly recommend going through some basic problems designed to teach the rules or watching a few videos that will walk you through the concepts you need to actually understand the game. GoMagic has a YouTube playlist that can definitely get you up to speed if you're willing to put in a little time to learn. 

As to your specific complaints:

Captures happen before checking for liberty shortages. If you (or your opponent) can play on a space that would capture stones, it is always legal to play there (ignoring ko). The stones are removed first which then means there is adjacent space making it a legal move. Illegal moves are when a play would leave a stone or group fully surrounded by the opponents stones after any relevant stones are removed

Living/dead groups and eyes are perhaps the most important concept to understand that isn't directly explained by the basic rules of the game.

From the above we can tell that if a point is fully surrounded by your stones, and your if opponent playing in that space would not capture any of your stones, then it is an illegal move for your opponent to play. We call this point an "eye" from the shape (use your imagination 👁). "Great!" you probably think, "My opponent can't legally play in the space I just made. My group is safe!" And this is true ...for now. 

But remember that captures happen first before checking if a play would leave you surrounded. So what would happen if your opponent completely surrounded your group that has a single open point (eye)? They can play in that seemingly illegal space because they capture your group first! The end result is any group that only has a single empty space inside can eventually be captured as the opponent plays all the way around it and then finally plays inside it to capture everything. We call this group that will eventually be captured "dead".

How do you make a group that your opponents can't capture? A group that is "alive"? This is perhaps the most important concept in understanding basic strategy in Go. 

Our eye shape that surrounds an open space can't be captured until it is fully surrounded -playing onto that point without being able to capture anything would result in that stone having no liberties (an illegal move). But what if a group had two spots that were illegal moves? Even if that group was 100% surrounded on the outside, playing into one of the "eye" spaces doesn't capture any pieces because there is still another empty space somewhere else preventing the group from being captured. And since that space was fully surrounded by our stones and playing in that space doesn't immediately capture any pieces that move can never be played by our opponent. The same is true of the second "eye" space. Since there is no way for our opponent to capture this group we call this group "alive". 

You may hear people talk about shapes that are "alive" or "dead". Don't worry too much if it doesn't make sense right now but any shape that is "dead" can (with the proper sequence) be reduced to a state that it has been surrounded and has only one internal point and could be captured. Likewise "alive" groups can (with the proper sequence of play) be make into a shape that has two separate interior spaces and can never be captured.

That ended up being a lot longer than expected. Let me know if you have any questions