Do the normal throws in SG have multiple active frames or just one?
All normal throws have 7f startup, 1f active, 28f recovery.
SDE had differing throws per character (eg Bella: 9f Startup, 5f active, 30 recovery) but it got standardized to the numbers mentioned above with the switch to SQG.
Be wary with info from the Wiki, it is partly outdated.
Does Skullgirls have any automatic throw immunity (as in, not a special property of a particular move, or the airborne state)? Like for example in Vampire Savior any time you are coming out of stun or during wakeup there are several frames where any throw attempt will not work, Victor's 360 will whiff, etc. It's very noticeable in VS because it's on the high end of throw immunity, but lots of fighters have some of it somewhere.
No
1. Can I just jump into the casual lobby matches ?
I have no idea what this question is supposed to mean
2. I currently play Valentine but I see the shortcomings of her already despite my own not-so-good performance.
At low level, anything goes. Tiers are meaningless, just play.
To put it simplest,
Char A, when played at 100%, has a strength of 1000.
Char B, when played at 100%, has a strength of 900.
Now, if you're a top player who plays a character to its full potential, this is a 100 Pt difference.
However, if you're new and only play 10% of a character, A would be at 100, B at 90 - just 10 Points.
Rather than switching chars, you could just learn more about your char, so you play 11% of your character instead. Boom, you're at 99 Strength which is basically the same as A.
On top of this, many chars have shortcomings which are far less pronounced at lower levels (say you only got unsafe blockstrings - at low level people don't punish, so it doesn't matter), or upsides which are difficult to utilize (eg Parasoul Tear tosses are really good but few people use them properly).
This means that while eg Solo Val is a shit 'team' at high levels of play, she may very well be good where you are at (people's offense is blockable so you're less reliant on a DP, and she has really good mobility+buttons as well as easy beginner combos, which gives you plenty success very fast).
I would like to ask what the benefits of playing a Solo character are and what each (solo) character can teach in the long run.
Solos teach you how to properly play neutral, defense, offense, etc etc rather than relying on assists to carry you.
Say you play Val+Filia. Updo saves you all the time. Opponent picks up on that, and the first time he touches you, he snaps in your Filia.
What do you do after Filia is dead and Val -now Solo- comes in, drop the stick?
You have to be able to play all your characters on your team as solos anyways, so you may as well start out practicing your chars solo.
In fact, if you plan to add a 2nd char (say, Fortune), rather than doing so I'd advise you to first practice playing Solo Fortune, and only to switch to the Duo after you have learned her to an extent.
3. In case, my other option becomes my favorable choice. Is Fortune/Valentine still a good choice or do I have to go with a 3rd character to lessen possible weaknesses ?
Again, anything goes
Trios are better than Duos. Solos are weaker than that.
However, Duos and Solos were FAR weaker in SDE than they are now. .. and KhaosMuffins got 4th place at EVO with Solo Fortune.
The game is balanced enough that you can run suboptimal teams to good success.