What can I expect I if connect several TTL outputs together?
You can expect to burn out one or more outputs. The open collector type of outputs are fine to connect together, that is known as a wired OR arrangement. If you have several TTL outputs and you want to combine them use a NOR or NAND gate depending on what level you want to see as the "winner".
floating output
No such thing, if it is floating it is not an output.