Holy smokes at the different methods and opinions (some of which I can say are just flat wrong, but that's neither here nor there) out there.
1) cleaning the rifle (NOT BORE)... a bolt rifle is pretty easy to maintain. No carbon or soot (or at least no enough to matter) in the action at all. Just keep it wiped down and free of dust and dirt. I would keep some form of preservative (i.e. rust inhibitor). It could be a liberal dousing of CLP, essox, or whatever you want to use. Some are better than others, but use something. I will add that if you're in the desert, use it sparingly.
2) greasing a few key areas is a good idea. I'm not familiar with Tika rifles, so it's hard for me to describe the cocking cam to you. Yes, grease on the locking lugs is a good idea but be conservative with it.
3) barrel break in... everyone swears it's voodoo. Some of the methods I've seen are rediculous (clean after every shot for 10 shots, every 3rd shot for the next 30, etc...). I do practice a kind of barrel break in. I clean after every shot for the first 5. Then I shoot 5 more and clean. Then I just shoot it. I don't think "breaking in" your barrel will make it last longer or be more accurate, but I think it will be easier to clean the copper fouling out of your barrel for the rest of the rifle's service life.
4) for punching holes in paper and hunting, .243 will provide more than 2k+ rounds of service life in a barrel. Sure, there might be some slight accuracy degradation at 800 rounds but you won't notice it unless you measure groups in thousandths of inches and anything bigger than .185 kills your chances at prize money. For your purpose .243 is just fine. BTW, bench guys don't hate .243 because it wears barrels out too fast. Most of pro bench shooters junk a barrel before the 1k round mark, or near it, anyway. .243 just isn't as inherently as accurate as a true bench round like .222 or 6mm PPC... plus it's a little on the recoil heavy side for true bench shooting.
5) cleaning the bore. I don't know your shooting habits, so it's hard to recommend a regimen. As far as precision bolt rifles, I shoot rather infrequently. Sometimes it's a couple of times a month, sometimes I'll go 6 months without shooting. If I'm in an "on again" kick, I don't necessarily eliminate all copper fouling between range sessions. I run a Hoppes 9 soaked patch through and "punch" the bore (run a bore brush through it a few times), then a run an oil patch to prevent rust. I know that I'll probably shoot again in short order, my time is limited so I don't always have time to remove all copper fouling right away, and my barrel doesn't foul bad in the first place so I usually don't see a noticeable accuracy degradation in my rifle until I finally decide that I need to thoroughly clean the bore. You absolutely can have an adverse affect by cleaning the bore too much, or more importantly at the wrong time, however. For a hunting rifle that sees little to no range duty, I wouldn't thoroughly clean the bore until after hunting season. Clean it up good, oil it, and let it sit. If you do go to the range just once or twice and put no more than 15 or 20 rounds through it between seasons, then let it be. If you put a bunch of rounds rounds through it before next season then yes, a good cleaning will be in order. Make sure to go to the range just before the next season begins to get a fouling shot (I like a few for good measure) in. Then don't touch the bore until season is out again. The reason why is your round impact out of a cleaned bore will usually be different than with a fouled bore. You shoot most with your fouled bore (obviously) so that's what you should sight your rifle in for. Some rifles don't shoot much differently between a clean and fouled bore... some rifles can be off by several inches at 100 yards. That could turn into 6 or 7 inches at 200 yards, which could be the difference between good shot and a gut shot.