I've looked at your other videos and I noticed that your DDD is probably a good choice for a secondary.
Anyway...
You seemed to approach too much using the fair. Which is not a good idea against anyone. Especially rob. When you're in the air, you need to use airdodge more than anything else. From what I've seen, you really need to practice using air dodges and side step dodges. It helps Snake drastically if you get it down. Doing airdodges from off the ground is an efficient way to dodge various attacks too. Looking at your first match, you got trapped so many times from Rob's combos. To get out of the combos, press jump and shield almost simultaneously. But, make jump go before shield. It gives you a bounce out of a bad situation and it gives some time to dodge attacks.
You seem to do your fair's at the wrong time. I would use it only if the person is off the stage, trying to get on. Practice making it so your fair doesn't make you float afterwards. You can do this by short hopping into a fast fall'd fair. Its pretty difficult to get the timing down for it though. Just practice in training mode, preferably over the edge, to get the timing down.
I'm not seeing enough grenades! Check this out.
http://smashboards.com/showthread.php?t=165922
That thread shows you various ways to use the grenades. I didn't see one which is unusual for a Snake to do. I'm not sure if they help as much against Rob, but, Its useful to pressure people by limiting the amount of space on the field.
Even if you got the Rob with the C4 some of the times, I don't think they were efficient enough. For example, you planted the C4 right on Rob in the first match and didn't try to set it off. If you did, you could of hit Rob with a bair or something. His percent was low enough to hit him with any aerial.
You should try using Nair more often. It probably would of worked out more than using Fair. Its good to use it right out of a jump or at the edge when the opponent is trying to get on.
By the way, your Bair looked pretty good. I just think you should of used it more than the Fair. The Bair can be used multiple times in the air which just makes a wall of pain to whoever is trying to recover. Probably one of the most efficient aerials Snake has.
You need to be more wary of the mines you placed. You ran into a couple of mines. I think the mines should be put more near the edge rather than the middle. But, if you place them in the middle, I would try to grab the opponent and throw them into the mine. Or pressure them with A jabs and Ftilts.
You were a little late when using your up+b. It gave Rob a chance to hit you when you were trying to recover. I would fly over him and airdodge profusely as I'm coming down to the stage.
Get used to the C4 recovery. You died a lot from using the cypher too low. If you know you can't make it, push the joystick down gently. If you tap B while holding down the joystick, you will drop a C4 and make it explode which will hurt you and send you up flying. But, it gives you a chance to recover.
When on places like Battlefield, I would use the mortar or Usmash more often. It stops Rob from doing his Nair.
If you take some time to read through the stickied threads and just practice with Snake. I'm sure you will get a lot better. Your videos are awesome. Just keep working on one character for a while and move to the next. Don't be choosing left and right on such short notice.
Good luck to you!