There is no risk from hands, even with saliva. There is just too much exposure with air, movement, etc.
1. So Is there any chances of getting sti from saliva after protected oral sex and also from slight genital to genital touch?
Saliva isn't the big concern with oral sex. STDs either reside in the throat, like gonorrhea or chlamydia, and the condom protected you from that, or they are spread by direct contact, like herpes and syphilis. The condom offers you significant protection against those.
If she had a syphilis sore in her mouth, for example, your penis would have had to come into direct contact with that sore in order for you to contract it.
You can get genital herpes type 1 if she has oral herpes, and you don't already have it, even if she didn't have an oral herpes outbreak. You wore a condom, though, and that offers enough protection against it that I wouldn't even worry about it.
The brief genital touching isn't enough to transmit anything. It takes significant rubbing or grinding or penetration to transmit any STD.
2. Should I go for STI test?
I wouldn't bother if I were you. You had condom protected oral sex. Your risk, if you had any, is very minimal.