More or less, any crankset will work with any derailleurs, chains, cassettes. I have an old 7 speed crank with 9 speed rings on a 10 speed cassette/chain touring bike. 44 tooth outer chainring shifted by a 9 speed Tiagra road front derailleur. In theory mountain bike front derailleurs are curved more to better line up with the smaller outer chainrings on mountain bike cranksets. But in reality, it doesn't matter. I suppose if you tried to shift 10 or 11 speed chains with 5 speed chainrings, you might have trouble. So try to get the chainrings close to the chain size. 9-10-11 can be mixed between chainrings, chains, cassettes. 7-8-9 can be mixed. About the only thing to make sure matches is cassette and chain. If using a 7 speed cassette, use a 7 speed chain. If using a 9 speed cassette, use a 9 speed chain. If using a 10 speed cassette, use a 10 speed chain.
About the only incompatibility is with the newest 10 speed Shimano mountain bike rear derailleurs. They do not work with road 10 speed STI shifters. But older 9 speed mountain bike rear derailleurs work fine with road STI shifters of any gearing, 7-8-9-10. Shimano 9 speed mountain bike rear derailleurs are really cheap, $20 Deore. So no reason not to use one. Low end Shimano front derailleurs, Sora, Tiagra, are also really cheap, $15. So no reason not to use those either.
You've mentioned using your left front STI Shimano 105 shifter to shift a triple crankset. It shifts a compact double crankset now. I'm not so sure Shimano STI can shift both double and triple. Shimano makes unique double and triple STI shifters in Ultegra and 105 models. So I'm questioning whether your crankset change will be as smooth as you are implying. I think you will need a new left STI shifter for the triple crankset.