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Which types of exercises are good to pair? I'll be doing that at my home and so far I owe dumbbells and barbell, bench is also not a problem because my friend has it.
Since I'm currently doing only BW exer. I thought on adding weights in 2 days of week as Jungledoc suggested me few months ago. I thought on pairing lats and biceps on 1 day, and on other shoulders and chest; but I read that chest workout already puts stress on shoulders and its not recommended to pair them. So now I'm in doubt, what to pair?

What are your goals? You don't necessary need muscle splits.

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depends.
Are you doing full body, or Push/Pull splits, or Upper Lower splits?

I'm doing full body variations from pushups, pullups, dips and leg workout and so far I got quite good results. Now I want to add some weights in the workout. Well my main goal is to have good physical strength and add a bit of muscles or I'll get rusty from all that sitting in my college. I'm also trying to gain weight since I'm one of the hardgainers if that matters.

Personally, I think bodypart splits are not suitable for you, or those goals. Get strong using big compounds, and sprinkle in some isolation if needed. For two days a week I'd suggest a full-body routine or then upper/lower split. Dan Jon makes a great simplification on must-have exercises:

Squat
Hip Hinge
Press
Pull
Carry

4-5 exercises. You can mix these in a lot of ways. Just do those once or twice a week. One or two should be maximal effort per workout.

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I workout 4-5 days a week depending how much I exercised in that week; I don't workout only 2 days a week if you thought that, or I read this wrong way :)
My plan was only to add 2 days of weights whilst keeping 2-3 days of full bodyweight routine. (1 day for legs (like squats and stuff - abs), other 1 or 2 dips and core).

you need to be more speific about what days you are doing what non weight full body work because that will interfere with weight days too, unless you are not stressing your muscles at all on the non weight days.

It should be something like this:

Mon-Weight
Tue-BW (Pull-ups, Dips, Abs)
Wed-Rest
Thu-BW(Pull-ups, Push-Ups)
Fri-Weight
Sat-BW (Legs, Abs)
Sun-BW/Rest (depends on 4 or 5 days a week)

I have many variations so my body doesnt get used to same routine, and I also use additional weight if necessary.

Or if someone has better idea, but Wed has to be free, because I have full-day college on Wed.

Is it maybe possible to even cut one BW day?
You could do the following:

Mon: Weigth lower
Tue: BW Upper
Thur: BW Lower
Fri: Weigth Upper

Core whenever you feel like it, 1-3 times a week. Or then you could try to do full-body routines with weigths and upper/lower split on bodyweigth or vice versa. That can be hard on your recovery, but you can always try.

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Prove the impossible!

I see no logic in sandwiching a Weight Training day between an Upper and Lower BW day, unless you give your muscles little stress on some of these days.

Why not just do Full Body 3 days a week, or Upper Lower splits, 4 days.
Maybe

Monday Upper Weights
Tues Lower BW
Wed Off
Thur Upper BW
Fri Lower Weights

If you train Friday morning and want to Saturday night, get in a Full Body BW session, or do some sprints

Ah, I should have read your first.
I'm scared.

Sure its possible to cut one day, I thought on doing 5 days because I think that will maximize my muscle growth, but if it won't do any good then it's ok :) I often play football/soccer on weekends so I think that counts a training too.

There's an increasing chance of too much overloading and overreaching, which can negatively hurt your recovery and thus your progress and muscle gains. Especially if done on higher intensities every workout. Muscle growth isn't about how much you can train, but on how you use that training time and how you rest between workouts. This holds true especially when the training background isn't really long. So you can add one BW day, but I'd strongly recommend it to be ligth and more of a recovery/deload-based

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Prove the impossible!

So you say; it's better to do hard 4 workouts and he rest 3 days, than adding 1 day more and increase injury chance. If that's the case then I'm perfectly fine doing 4 hard workouts. I got one more question. If i follow routine as you suggested it above, how should I do leg workout: With or without weights? My leg workout consists of (squats,lunges,calf raises and wall sit)

So if I've got this right you will continue with some bodyweight exercises but are going to add in some db/bb stuff.

Your goal is strength, and getting "some muscles" tends to follow from that.

If you do nothing else, do squats twice/week. If you don't have a squat rack, build one. The example below can be simplified, you can use sand instead of quickcrete, 2x4 studs instead of 4x4 posts, and so on.

http://www.endofthreefitness.com/crossf ... ess-stand/

After that, deadlift.

Then the usual suspects: press (you can use your squat rack for pressing as well), bench, pullups, rows.