I'm Muslim, I use Md. as for Muhammad. So when submiting to journals, should I stick to the 2nd & 3rd names? I'm currently facing problems in submitting to arxiv.org which asks for only first and last names.
This shouldn't really be a problem these days in most places, because the entry fields on most web-based entry forms are smart enough to recognize and accept spaces. Thus, even when the site asks for a first name only, you can put in "Md. [Middle Name]" as your first name.
As Dave suggests in the comment, unless you have a really uncommon last name—one that doesn't show up in ISI or arXiv.org searches at all right now, you're better off having parts of three names show up. It's also helpful to keep your professional name fixed throughout your career. (In other words, if you want to go by Md. [Middle] [Last], use that same form whenever possible.)
My advice is to use at least 3 names (including your surname) so that you will be uniquely identifiable. It probably doesn't matter if you do not use your first name unabbreviated. I know a few researchers whose names are of the form: C. Harry Kay. I also know of researchers who go by a single name (Robby, Arvind). So just fill in whatever names you want , abbreviated or not, into the first names field.
Make sure you use the same configuration of names for your entire career, so that all your papers can be linked to you (I made this mistake).