https://addons.mozilla.org/en-US/firefox/addon/bartab-plus/ does the same thing (actually a little better in the implementation) on Firefox. Once you install, go into config for it and set how long a tab may be idle before it auto-unloads. Unloaded tabs are shown slightly dimmed in the tab bar. You can also right click tabs (such as gmail / youtube / etc) and force them to always stay loaded, so your email / music streaming / etc aren't impacted.

Combo it with https://addons.mozilla.org/en-US/firefox/addon/tab-groups-pa... that lets you organize your tabs into groups and you can have hundreds of well organized tabs without using much memory at all.

No need. Make sure "Don't load tabs until selected" option is enabled and then restart the browser once in a while.