Another dilema: the trade of the fianchetto bishop for the rook

Surely the rook has more value than the bishop, but there are positions in the game that trading this two pieces is not clear in our benefit.
So, my dilema about this topic begins when I'm playing with black and there is an oportunity to trade my king side fianchetto bishop with the oposite rook (in a1). In the endgame I see no problem with earning the exchange but what about in the early and middle game, when there are still the queens and bishops in the game? Don't you get scared by giving the long diagonal to your opponent and with that, a very clear "highway" to be attacked? Or do you calculate this every single time? But what do you do if you are playing bullet or blitz, where there is little time to calculate?
I leave this now to your discussion.
Cheers. 

Of course it will always depend on the individual poosition. But, from a general consideration, the move ...B(g7)xR(a1), first if the opening you are in is one of the openings in your opening repertoire then the decision is easy because you have been in that position as Black many times. Your Middlegame and Endgame visualization pattern memory banks will shortcut detailed analysis of the position. Regarding bullet or blitz, you have highlighted one of the reasons that strong players play bullet or blitz. That reason is that it triggers the visualization patterns mentioned and reinforces those visualization patterns in your mind.

The same holds for ...B(b7)xR(h1).

If the position is one from an opening that is not one the openings in your opening repertoire, then it will require detailed analysis of the position. Your 5 visualization pattern memory banks will be a great aid in analyzing the individual position no matter what the time controls.

I think as long as your queen is in a position to defend the squares that your bishop would have been defending by being fianchettoed then it's okay, otherwise I'd find it risky.

If the position is a bit more simplified, I would go for it! You can also try to walk the king to the queenside if it is a bit safer over there and start a kingside attack.

It is almost always correct to trade your fianchetto bishop for a rook on a1.

 There are exceptions as with any chess rule.

There are thematic exchange sacs (for black) in some openings where White has a K-side fianchetto, I seem to remember something in the Catalan?

Black Queen recaptures on a8 with bad intentions on the long diagonal vacated by thed now dead bishop.

Probably almost always correct to take the rook, but always with some circumspection.

I'd just always play it safe and take the exchange. You really can't be worse off up an exchange unless you're incredibly underdeveloped and your opponent has a strong attack.

If you're up an exchange why not just trade to a winning endgame?

Whether or not it's a good idea to take the exchange will depend on the concrete position on the board. But to be honest, I'd be inclined to take the exchange in all cases where it doesn't seem to (almost immediately) backfire on the diagonal in question.

there are very few times when i would trade, all of these are red flags.  

1. their rook is undeveloped

2. they have their queen and bishop of same color and you will castle on the side where the bishop was

also the bishop has amazing scope and is worth more than a rook, maybe even a queen

An undeveloped rook is temporary, and if a bishop is stronger than a queen you're doing something wrong. I'm sure there are cases where it would be best not to take the exchange, but unless you're a very strong player I wouldn't worry about that and just take the exchange.

that's all theory, and after Bxf8 Qxf8 black has good chances too

An exchange is only a real advantage in the endgame, where rooks are free to roam around and their mobility isn't restricted, after 14.Bxf8 Qxf8 15.Bc4 wouldn't white be able to start a series of trades and use the exchange to his advantage? Besides, what else would you suggest white do if not take the exchange here? Not to mention black has the inferior pawn structure.

Yeah, an exchange is an exchange. With no compensation (i.e. an attack against your now weakened squares around the king) it's a winning position.

theory

When you're having trouble evaluating an exchange remember what you need to weigh are the pieces left on the board for you vs the pieces left on the board for them.  In a sense the pieces coming off have nothing to do with it.

Could you expand on that, I don't really understand what you mean.

Comparing the pieces that come off the board is just a useful shortcut for uncomplicated positions... for example winning a queen for a knight.  When there's a difficult decision you have to, as FirebrandX says, compare the future position to the current one, that's all.

"Look at the pieces on the board not off the board" is a common bit of advice actually.

Oh, but I said "weigh the pieces" didn't I.

Well if you want to be rigorous, of course just evaluate the position... the pieces are just part of the evaluation.

But I also have a habit of looking at all my opponent's pieces and putting them on a scale in my mind so to speak.  The more active they are the "heavier" they are.  If I'm falling behind in this overall weight, I tend to avoid contact between the armies and work on improving my position.  If I'm getting well ahead I'll look for sacrifices.  Specifically sacrificing to activate my worst pieces or sacrifice to exchange off their best pieces.  Opening, middlegame, endgame, I think this is always useful.

IMO strong players obsess over piece activity.  I feel like you almost have to be paranoid about it :)  The downside to this habit is sometimes I miss tactics if I'm feeling underweight (so to speak).  Very often tactics come from active pieces, but sometimes forcing sequences seem to appear from nowhere.

Anyway, if I'm having trouble deciding on an exchange like the OP mentions, and I've evaluated the positions and thought about it and I'm still unsure, I do this weighing thing sort of like a blunder check.  Using the future position, all your non-pawns go on one end of the scale, and all my non-pawns on the other side.  That's what I meant by the using the term weighing.

Thanks for your help so far.

There are a few games in the past that I did with sucesseful and terribles outcomes, due to this topic. There are things in chess that are clear cut: "don't do this, because it's bad" but the trade of the king side fianchetto bishop for the rook is very unclear, sometimes is awesome, sometimes it can be your doom. Even in some few master games I saw this happening!

Cheers.