Hi, and welcome to cartography ^-^ Sounds like you've got quite a project on your hands. Retracing your map over and over can definitely be pretty boring; Inkscape (vector in general) is a great way to go since you can scale to whatever size you need. As for your questions:
1) lat-long lines are annoying at best - I would recommend G.Projector (Global Map Projector), from NASA. It's available for a lot of OS's, and it not only can project any image (say, that equirectilinear map you have ^-^) in a variety of different projections ranging from Azimuthal Equidistant to Hammer to Winkel Tripel, it can also project lat-long lines at a variety of degrees (2-10, 15, 30, 45, 90). You can set the color and "weight" (opacity) of the lat-long lines, and even center the map at a specific longitude degree (E). You can overlay different maps or images onto the base map as well. You will need Java to run the program, but it's standalone; you won't have to install anything.
2) I'm afraid I don't know Inkscape very well (I use Illustrator), but there are some excellent tutorials as well as just basic advice and tips in the Tutorials section of the forum.
From my limited knowledge of Inkscape, you can use the "bezier curves and straight lines" tool (Shift+F6; the blue pen 2 tools above the 'A' on the left). Left click to place your first and second points, and right click to end the line. Unfortunately, that's about where my helpfulness ends in regards to Inkscape -_-;
3) Personally, as an avid lover of all things art and illustration, I would say "GO FOR IT!", especially since that student discount won't be available to you much longer. On the other hand, it really depends on how much you'll be using those programs, and for what - for illustration (say, a world-building project with maps and illustrations), I would recommend Illustrator and Photoshop and leaving the rest of the programs in the Suite for another day. Dreamweaver, InDesign, Flash, and Fireworks can be great programs, but unless you're going to make a career out of this, you don't really need them. Now, if you plan on making a fully-customized website with interactive maps and detailed, custom-layout PDFs/documents, go ahead and get the whole Suite. Otherwise, there are tons of free and less-expensive-than-Adobe products out there.
Having said that, I have the Adobe Creative Suite, and I've still downloaded and am messing around in both Inkscape and GIMP - they might not be "almighty Adobe" products, but a lot of people use them and if you have the time (and inclination and patience), I think it's worth it to see what other software can do.
I hope my reply isn't way too long, and that this helps! The forum is a fantastic place to get answers, and don't wait to start posting your maps! We need more hand drawn maps, even if you plan on going digital with them ^-^ Good luck with your project!