How can ryu.......

advance across the screen safely?

Toss a LP hadouken and dash behind it, or walk forward and c.MK your opponent’s toes.

If you just talking about moving from one side to the other to escape a situation, just Air Tatsu

Instant air tatsu: :qcb::uf::hk: or if you can’t get the hang of it (I can’t do it all the time), jump and immediately do tatsu as you’re leaving the ground. If you have an square gate arcade stick, the easiest way to think of it/do it is riding the gate (it should be one quick, smooth motion though, not jerky as if you’re are actually riding the gate) from up-forward to back: :uf::r::df::qcb::hk: (any kick version works, it’s just that HK and MK are better). You can do it by simply doing the reverse of instant air tatsu, i.e. :uf::qcb::hk: I find though that I sometimes get lazy/sloppy and get the inputs wrong so doing a whole motion from up-forward to back is better for me, and it can be done just as fast.

Pick Seth.

walk and block

air tatsu is good for getting over your opponent.if your trying to advance against fireball spammers HK tatsu is good for going through and getting a hit if u time it right.just a tip for this though,it cant go through goukens FBs and guiles recovery is really fast on sonic boom so be careful with it against him