To answer your questions directly;
1- To check the chain for wear you need a ruler (or better, a micrometer) and the ability to spin the rear wheel. The spinning can be done with just the side stand and a helper. You're looking for a stretched chain (distance between a pre-determined number of links described in the manual) or tight / kinked spots. To adjust the chain you'll need wrenches or sockets in the correct size for your bike's axle. I'm unsure of the actual adjustment method utilized by a CBR125, wrenches are likely required here too.
2- I'm not clear what you're asking here. If it's time for an oil change, change the oil (and filter). If it's not time, but the oil level is just down a bit, top it up. If in doubt, it never hurts to do an oil change. Your bike CAN'T be as complicated as mine for an oil change; 2 drain points, 2 screens, 1 filter. I ended up changing mine on a whim yesterday as my coolant level had gone down inexplicably and I suspected a water pump shaft seal issue. Turned out that there was no coolant in the oil. I suspect I had a bit of air in the cooling system from a rad pull a while ago and it finally "burped" but now I have fresh oil and filter on board and the warm, fuzzy feeling that comes with it.
3- See below.
Canadian Tire has sales every week on socket sets, pick up one of the larger ones if you can. Buy a torque wrench when they go on sale. Buy a screw driver set.
Buy an oil drain pan and a funnel and a lot of shop rags.
Check kijiji for front and rear stands.
Stick with the Mastercraft Maximum line and you can't go wrong. Break a tool? Just bring it in and get a replacement on the spot, not like others such as Stanley where they have to send it away for a replacement. Of course brands like Snap-On are even better, both in quality and customer service / replacement, but you'll pay much more than you need to as a back yard mechanic. Sign up for Canadian Tire's sale emails and you'll scoop some great deals (I'm looking at the tap & die kit on sale right now). A set of good stands (NOT Canadian Tire's) is priceless.
I learned online and through service manuals. Get some tools and tinker around, you'll figure it out.
^^ this. And a bit of help / advice from friends.
Every time I tackle something I've not done before, I realize that it's not as difficult as I thought. It's also great to be able to see how everything works. My 2nd bike had worn rings. I made it a winter project to pull the engine out, put it in my basement, rip it apart, send the block out to be bored out 1 size over, replaced the pistons with the corresponding size, then put it all back together with refreshed / new parts where applicable. That was in 1996 (or 97) and that bike is still running like a top today (a friend bought it). There were a lot of borrowed tools involved during that job. Each job I do has the opportunity to provide justification for a new tool and down the road, using those tools will save you having to pay someone else to do the work for you. The service manual is your friend and will outline what inspections you should be doing and when.
I can't remember the last time one of my bikes went to a shop other than for an alarm install as TD wanted it professionally installed (EDIT; my TL went into the shop in 2003, but that was for a warranty job to have the cracked frame replaced).
I look at the maintenance as part of the hobby. This is a typical winter for my bikes (this bike was torn down even further than this but I forgot to take a pic);
