Google for "unicolor roller" as that's what you have. You can get a motorised base to run it on and not wear your arms out.
Nope. Tube can be wet when you put the next piece of paper in there, just give the paper a 20s pre-wet so that it's ALL wet, not just the bits that got dripped on. Keep in mind also that tube processing will oxidise developer so it will not last very long, but you need very little compared to trays. I use 100mL at a time of Multigrade 1+10 (I think 60mL is enough for some 8x10 drums) and run it through the tube 3 or 4 times before discarding. Even if you use 1L at a time, it'll still only last maybe 10 processes before it dies because it's not the paper that's exhausting it.2) It is easier to do a couple of quick prints with the tube, because it isn't necessary to set up and take down as much stuff. It is a bit of a pain though to do much more than a print or two, because you need to thoroughly rinse and dry the tube before each print. I solve that problem (when I am using the tubes) by having a number of them, plus space to air dry them between rounds.
Your enlarger really is only good for 6x6 (but it will make perfectly good 8x8", maybe 12x12" B&W prints with that 4-element lens); neither the lens nor the condensers will cover 6x7 properly. Good 6x7 enlargers are pretty easy to find though, usually for $0 to $50, maybe $50 to $100 with a good 6-element lens (Componon-S, Rodagon, EL-Nikkor); you want 80mm for 6x7. You will want a dichroic (colour) diffusion enlarger if you ever want to print in colour, easily recognisable by the presence of cyan/magenta/yellow knobs. And they're (IMHO) easier to use for B&W printing than a condenser enlarger with separate contrast filters.
My FAQ has a printing howto that will probably answer a bunch of your next questions, or better yet, get a copy of Way Beyond Monochrome. More modern than The Negative, plus it covers the stuff in The Print too.