I have yet to find any comprehensive, excellent tutorial series for this, but Greg Wilson's writeup from 5 years ago is still the best I have found. https://medium.com/@somegreg/orienteering-mapping-...
Short answers to your specific questions...
1) .las or .laz (the same data as .las, except in a compressed format) files are the only file types that you want to get your LidAR in. These files contain the raw LiDAR point cloud that you can then use to process out whatever you want (like the Digital Surface Model (DSM), Digital Terrain Model (DTM), etc.). The Metadata file for your .las and .laz is also very helpful to have so you know the projection and units or your LiDAR - but this can get very messy very quickly.*Note that some jurisdictions will only provide ground points only LiDAR (still as a .las or .laz), which will mean you won't get any vegetation information just contours - instead get the "full point cloud" version (still as a .las or .laz).
2) LiDAR files are really, really big. All that tiles are, is that instead of taking the entire LiDAR data collection (that could quite literally be terabytes in size), whoever is distributin the LiDAR breaks it up into "tiles" of more manageable sizes. Just get the tiles for the area that you need. You shouldn't*
need to do any conversions of your .las or .laz files to make them work with Karttapullautin (KP). *Although I think you are based somewhere in the states, so depending on where you get your LiDAR from, the units embedded into the LiDAR file might be in feet, not meters, which will wreck havoc on the scale when KP tries to process it.
3) Well ... OpenOrienteeringMapper and time are your friend. The map product strait out of KP will be totally usable for training (sort of), but if you import it into OOMapper, then the more time you spend improving the map (drawing trails, buildings, water features, etc. that KP can't directly map [other than sort of based on OpenStreetMap data, but it is strongly recommended to do this processing in mapper instead]) the better your map will be.
If this isn't enough to help get you started, or if you run into very specific problems a little bit down the line, I could probably do a Skype/Zoom/Teams call and help you out.