To upgrade units which have already been trained, there is an 'Upgrade' button under the main screen unit overview (the selection panel in the bottom left corner of the screen). It may be hidden in the '>>>' menu on that panel. Upgrading units will cost you gold and resources for equipment upgrades, and gold for unit size upgrades.
Be advised that, as far as I know, you can't choose what you upgrade to, meaning that you'll upgrade to whatever the computer believes is the best equipment for your units (weapons go for highest combined attack in the same weapon category - swords to swords/axes to axes/clubs to clubs/spears to spears/bows to bows, not spears to clubs or something like that, while armor goes for highest defense rating; no other bonuses are considered, so if you made a dodge-based unit which really needs the dodge from the Monk's Robe and the initiative from the Soldier's Boots, don't upgrade your armor). I also don't believe that there is a way to tell a unit to only upgrade certain items (your options are armor, weapons, shields, and unit size, but I don't think that design choices in the Unit Design screen affect this - i.e., if you tell a unit to always use Altarian Leather armor and 'best available' boots, when you order that unit to upgrade its armor you'll lose the Altarian Leather if you have chain or plate available, rather than keeping the Altarian Leather and changing the boots - but I'm not certain, as I don't usually care what my units are using as long as I can keep them alive and fighting).
I do not need to build roads to connect cities like in Civ for ressources right?
Correct, it is unnecessary to build roads from resources to cities in order to make use of the resource. Be advised that resource structures are placed in the build queue of the closest city under your control (if you order construction of a resource improvement, and then found a new city which is closer than the old city was, the construction order will shift to the new city), and the basic ones usually take 3-5 turns to complete on normal pacing. This means that if you aren't paying attention to which cities your resources will be assigned to, you can significantly delay city development, and it can take a very long time for a new or high-unrest city to complete large numbers of resource improvements. Unfortunately, the only way to control resource construction assignment cities is to chose when and where you build your cities (potentially also razing some cities if you really, really don't want the resource to be improved by that location).
I do, however, tend to like having roads that at least come close to the resource, as it makes defending the area against raiders much easier, unless the resource is in a secure area. Automatically generated roads going between cities or headed off to nearby outposts are usually sufficient for this, though sometimes I like to make my own additions to the automatically generated roads.