“Split clips” – do you mean razor ? Ctrl -K (customise it to a single key if you want). Maybe you mean something different by “split clips”
There is a short cut for a Trim to the CTI position. Do not think there is one that extends to the CTI position though
You can drag the edit point in a number of ways including using the slip , slide, trim, rolling edit tools provided. Try CTRL Drag and Alt Drag for a start.
Your last request is too personalised to your work flow but copying & pasting clips is as easy as CTRL-C and CTRL-V