Those errors are not a plug in fault, but hosting service (mis)configuration and thus giving you even less writing privileges than a regular shared hosting provider should.
Inability to write to stuff like .htaccess is bad if it’s not your choice.
To see whose fault is it, use your FTP program to change the writing privileges on .htaccess (and the other problem files) to 664. If you get an “access denied” or “not enough privileges to…” then your hosting service has restricted you too much.
If your FTP program succesfully change to 664 (which means: Write (owner) Write (Group) Read (Everyone) then it was you who did something wrong and write protected the files. W3 TC is not to blame.
W3 TC indeed is a very delicate plug in that requires either a good hosting provider or (and) knowing some more technicalities than the general WordPress plug in usually requires.