A Solaris machine has ksh as the default shell, I believe. Ksh doesn't have the sophisticated interactive feature you may be used to if you've used bash or zsh before. If you want a comfortable environment, install zsh or at least bash on the Solaris machine. If bash or zsh is already installed by the system administrator, use chsh to switch to it. If you install it yourself, you won't be allowed to use chsh, but instead you can switch shells inside your .profile (make this the last thing):
case $- in *i*)
## This is an interactive shell, try to switch over to a better shell
if whence zsh >/dev/null 2>/dev/null; then exec zsh -i; fi
if whence bash >/dev/null 2>/dev/null; then exec bash -i; fi
;;
esac
If you decide to stick with ksh, its configuration file is ~/.kshrc, that's where you would define aliases. (Note that aliases are for each shell instance, not for a session, so they don't belong in ~/.profile).
The Backspace key should work out of the box if everybody left things well alone. Unfortunately, many OSes ship with settings that make double sure everything works as long as you're using the same OS everywhere, but break the automation that would otherwise make things work across remote logins. I don't know which of Solaris or OSX is the culprit. If you don't feel like investigating, you can tell the Solaris shell that the “DEL character” deletes to the left with this command in your ~/.profile (this will do the wrong thing if you log in from a machine where BackSpace sends ^H).
stty erase '^?'
The Escape key doesn't normally quit any text mode application. The usual man page viewer is less, and its quit command is bound to q.