Fish has exactly one user controlled config file which is named $HOME/.config/fish/config.fish by default. Fish also has an export command for compatibility with bash/zsh/sh but it just a thin wrapper around the fish form:
set -gx VAR value
As for bash aliases you have two choices: turn them into abbreviations (see the "abbr" command) or functions. In fish you can define a function with its "alias" command but that simply turns
alias myalias some_command --arg1 --arg2
function myalias; some_command --arg1 --arg2 $argv; end
As Glenn Jackman pointed "fish is not bash". It is not an improved bash. Switching to fish isn't hard but does require a little effort. I made the switch 13 months ago and think it is worth the effort.