You aren't the only one. Ubisoft got some problems with keeping the online servers up and running.
You can see their twitter account for news about the situation. As you can see it's full of "it's working - it's not working - it's working again - oops, it's off again" messages.
You really ought to be clearing radio towers; they reveal the minimap in the area, give you free guns, and provide a nearby respawn point (though you can't fast-travel to them). The latter benefit isn't that useful if you're on PC - even though it's not listed in the controls, F9 will quicksave and F11 will quickload, unless you're currently in a mission area in which case the game seems determined to become Call of Far Cry.
Clearing outposts is a take it or leave it sort of thing - as I'm sure you're aware, every cleared outpost becomes a fast travel location which can make getting around the island significantly easier, and provides you with an automated store for ammo refills. Some outposts have collectibles in them, if you're in to that sort of thing.
One less-obvious benefit of clearing outposts is that doing so usually unlocks some local quests. Normally, these are the "go here, stab man with knife" sort of things, or random local color; usually not the sort of thing that's gamebreaking to miss.
However, the big thing you're missing by not clearing outposts are the rare Path of the Hunter quests. A significant number of them have you hunt down rare, adjectival beasts that are impossible to find otherwise; those beasties are used to craft top-tier equipment like ammo pouches or loot rucksacks. If you want to have the biggest bags of all (and really, who doesn't?) you're going to need to clear outposts.
So, that being said, in your situation I would recommend the following:
- Activate all radio towers, unless for some reason you object to seeing the minimap in which case you should become friends with quicksave/quickreload.
- Use a list of Path of the Hunter quests to figure out which outposts to liberate; the ones for {adjective} {animal} are for rare animals you won't find outside of these quests (e.g, Black Panther, One-Horn Buffalo). Liberating these outposts should also give you a smattering of fast-travel points in useful areas on the northern island, though there aren't as many on the southern island so you'll probably want to grab a few extra there.
Best Answer
Owning the gun is different than currently having it equipped. You can own all the guns, but only have up to 4 equipped at any given time. See this question for answers on how to equip guns you already own.