That blue writing you mention is an old bug, that just won't die. It doesn't appear very often however and it is not dangerous in any way, more of an annoyance.
Now the second bug you describe is even more familiar to us under the name of "Falling off the edge of the world". It mostly happens when you lag and server thinks you are under the level of the actual floor, from what I know. It is also bound to be fixed somehow, the devs are looking into this since it bothers a lot of people.
For now, try to avoid doing hit and run attacks in places where that falling has happened to you until the bugs get fixed. This is still a game in development and for a pre-alpha stage, it is not uncommon. I would rather have expected even more bugs in this stage of development honestly, so it's only bound to get better and bug free with time.
/offtopic This should have been in the Technical Help: IN GAME bugs (after loading world) section in my opinion.