Yes, you should take the reel apart & clean and re-oil it, but you don't have to do it after every fishing trip. A drop of oil on the worm gear for the levelwind & maybe a drop in the end of the reel handle grip will do before each trip. But in the spring before your first trip of the year, & after about a dozen uses (the frequency depending upon how dirty/gritty the reel gets), you should break the reel down, clean the old lubricant off of the reel parts, & put fresh stuff on. Use oil on the levelwind worm gear & worm gear ends, the spool end pins, the sleeve for the handle shaft, & (if you have one) the bait alarm gear. Use reel grease for the gears in spring, summer & fall. If you use the reel for ice fishing instead of storing it for the winter (a lot of baitcasting enthusiasts do use baitcasters through the ice), use oil instead of grease on the gears, too... makes it a lot easier to crank in zero weather. In warmer weather, though, the gears should be greased. It doesn't hurt to wipe all of the lubricant off before storing it for winter, either. If you can't afford regular reel oil, 3-in-1 works. If you can't afford regular reel grease, Vaseline works in its place just fine. The best thing you can do for your reel is to keep it clean while you use it. Never lay your reel in dirt or sand. Granular grime is your reel's worst enemy. Also avoid letting it go in the water. Particles of dirt & sand float around in the water, & the liquid will carry that stuff right into your reel's innards.
As far as using Spiderwire on your baitcaster: as I've mentioned elsewhere in these forums, baitcasters were originally designed for no stretch, noncoiling line (made out of different materials in the past, of course). Monofilament was originally designed for spincasters & spinning reels, & baitcasters couldn't really handle mono until the early 1970s. And even today, baitcasters still work better with no-stretch lines. So, yes, Spiderwire would work a little better on your baitcaster than mono. It backlashes less... but when it does backlash, it's terrible! You will need to use some mono for backing... at least a yard of it... because mono will grab the spool, & Spiderwire won't. So put the mono on first, then tie the superline on it with uni-knots, & finish spooling up. If you want to save money, you can keep the spool up to halfway full of mono (depending upon your reel's line capacity), and have the top 50 or 100 yards Spiderwire (the superlines are much thinner than an equal strength of mono, so putting at least 50 yards on top of a half-spool of mono should be no sweat).
Hope I've helped you, Gill. Keep the line on the reels fresh & the hooks sharp. God bless you. -Sonny.