Tank battles you need fodder, dogs conscripts. Lure tanks to base place pillboxes or sentry as fodder. Dont command tanks to shoot. Let them run past on their own. They're more efficient at shooting on their own. Only time i recommend clicking to shoot is if you see one of the enemy tanks with low health bar on the edge of his grouped tanks. Click, kill, run. There's a lot more to good TC but for the most part you'll just need to practice to get good at this.
As for bfs, defense structures like pillbox and sentry or fodder like rockies or send spy plane above and then rush in and attack. It's very tricky though and requires some skill. If you're allied a good amount of prism tanks will take out a bf but if you're playing toe then i'd imagine his allies or him would have massed equal amounts of prism aswell.
TOE is a lot different then regular competitive games. Play normal FFG to work on your skill.
Also, here is a basic Soviet Build-order that should work on most maps.
Power Plant, Barracks (+ 2 dogs), Ore-ref, Warfactory (+ 1 miner then Rhinos), Ore-ref (build closer to gems or ore then sell first ore ref), Ore-ref (Sell another one of your ore refineries). Once you got 4 miners then make radar, then either tech up (battle lab, nuke reactor, industro plant) or build multiple Warfactories for tanks to build faster. This all depends on what map and player you're versus.
Again Depending on map or players you're versus and who you're allied with and what you feel you might be able to pull, you can also skip miner from warfactory and go straight tanks. Try different strategies like selling MCV with 3 or 2 miners. Work on Economy. For instance, never let your cash flow go to zero. Watch miners and if you feel you're fixing to go broke (usually when your cash drops below 800 or 700) send the miner with most cash early to ore refinery.
Work on good build-orders first then worry about micro and tank control. You need to learn the maps. There's a ton more stuff also and i'm only an average player but I can help with what I know.