Keep in mind I have not played COH2, but played a lot of COH1. Notes below relate to COH1 but from what I have seen on youtube COH2 plays fairly similarly. Some Company of Heros 2 tips!
Use retreat liberally. Saving units and ceding ground is generally better than losing units. Reinforcements are cheap compared to buying a whole unit. For instance, if your units are all in one area and you hear mortar fire it might be better to simply select them and retreat. In COH retreating units took less damage, moved faster, etc.
When a group of units was selected in Company of Heroes you coold “tab” between all selected units using the tab key. This was very useful for issuing different orders quickly. tab, move, tab, attack, tab more, tab more, tab move. Saves you having to select individual units with the mouse.
Also in COH1 you could “jump” to the most recent.. action using spacebar. There was also a feed on the left hand side of the screen. When the announcer says under attack/whatever press space. Your POV should jump to the current engagement. This is probably not the ideal way of playing, but I am not a hardcore RTS guy and it was suitable way to quickly cycle through stuff.
Since you were having problems with mortars specifically the following might be useful. Range and line of sight heavily changed how accurate/effective artillery was in COH. This means a mortar at long range shooting into the fog of war was unlikely to hit what it aimed at. A mortar at long range with units spotting for it was somewhat accurate (however due to the travel time of the shells you could move your dudes before they landed). A mortar in close with spotting + support was quite dangerous due to accuracy + fast shells.
If you cannot see any other troops it is possible the other guy is spotting with a sniper on hold fire. This could end up being a popular tactic in Company of Heros 2, especially if the mortar has been buffed compared to COH1.
Which brings us to snipers. Ideally you should put them on hold fire+cloaked, especially when you first deploy them. This stops them randomly attacking. Keep them close to your front line guys and be ready – if you drop an enemy squad to low member numbers use the sniper(s) to try to take out the remaining dudes and eliminate the unit completely. This can be a large setback if it happens early enough in the game as you will be one unit up (provided you haven’t lost any to that point).
After that first engagement you can be a little more brazen. It is probably good to be aggressive for the first few minutes after initial uncloaking. This way you can get some quick kills in before the enemy gets out a counter (sniper/decloaking unit). It is even possible to play uncloaked, giving faster movement, just keep the sniper behind your other squads. After this first few minutes of this, if you feel that the opponent is going to try to counter you should cloak up and move between each shot. The common counter is another sniper on hold fire who uncloaks + kills your sniper when he shoots. Moving between shots, or even waiting a long time will prevent your guy being taken out.
While the learning curve is steeper I would heavily suggest playing 1v1 over the team game types. It is a lot more controlled and makes analysing your game much easier. Are you losing because of cut offs? Because of infantry out of cover? Because of rushing into MG?
Company of Heros 2 looks to be the goods.