Is having more than one hero pretty much mandatory after a certain point? I got to around 5 shards, and just started getting steam rolled. Wondering if I'm doing something majorly wrong. Obviously, I need to change up my tactics, I just can't figure that out what. The general steam rolling the map seems to have it's limits, heh.

Also, on some maps, the enemy castle will be guarded by hordes of bad ass dudes, like level 4 wizards. It just seems impossible to conquer in this situation.

Early campaign has its difficulty artificially lowered - for comparison try to start single player game. First ring - 4-6 units, second ring ~8, third ring 12+. Campaign even at third ring would have 6 units.
You are slowly getting to the point of standard game difficulty.

Your most successful hero would change from shard to shard (good spell early - mage would be priority, good egg - commander to hatch it, good bow - sniper...)
But, overall. you use your main hero to clear sites, and backup heroes to find sites for him.

As for strong guards - most of them can be cleared by suicide sniper(to kill most annoying target(s) + solo warrior.
Maybe these topics would be interesting for you
http://www.gog.com/forum/eador_series/scg_i
http://www.gog.com/forum/eador_series/society_common_game_2_iron_wall
http://www.gog.com/forum/eador_series/society_common_game_3_manly_guys_doing_manly_things

You just need a scout and a warrior. Commander and wizard take too long to find good equipment and become strong, only useful on shards where you are forced to 'turtle' your way to victory. On the other hand, if you do happen to find a good flag early on (hahahah, yea rite!) , a commander can be significantly more effective than a warrior.

Anyway, i feel the key to success is through building up a powerful scout with a good bow and long range with double shot accompanied with a warrior with circle attack (via berserker). If ever you hit a brick wall, use the archer in suicide attack accompanied by as many 'cannon fodder' as he can take and pick off all the most annoying units then launch the second attack with your warrior.

To avoid getting overrun by AI, well the basic answer is that you have to keep your first hero's fighting as much as possible right from the beginning, because you have to make sure your hero experience level does not fall too far behind those AI hero's in order to stand any chance of stopping them. So, try to reduce traveling and exploring as much as possible, and your third and fourth useless hero's can do exploring to find work for your important hero's.

Another noob question (although I have started the campaign several times but not went too far): is it possible to role-play on Expert (middle) difficulty? By role-play means if you play good then you must not buy evil troops (no barbarians or rogues) and in the events to try to take the most "good" option. When playing on easier difficulties it seems possible, but on Expert I always seem to go bankrupt when I hire only Swordsmen, and I expand so slow in order not to lose them that the enemy shows up at my door with superior level and troops.

It is possible, but a bit problematic without knowing requirements for medals
http://www.gog.com/forum/eador_series/award_medal_details_request_to_russian_speaking_friends

The deeper you are in the campaign the easier it gets. Good karma events (pilgrims for free artifacts); shard bonuses (crystals; buildings like library; units like Healer or Fairy) would help.

But getting medals very early will increase the maintenance costs plunging the balance in the negative, and then losing a single unit can be irrecoverable, since all the money is spend on initial units. How can you deal with the initial funds granted you can make a mistake like losing an unit or two?

I don't lose initial units.
https://www.dropbox.com/s/3k3twkv7p4x18b6/swordies.mp4?dl=0
If you aren't sure in your skills, start with barbarians/brigands.

When you would get more game experience, starting with a scout is a safe bet. You can get 2 swordsmen+healer with only one cleared site. these 3 units+ scout+ spells from library can clear first ring (leave lizardmen for last). With some medals - second. Get third swordsman - go to third. Price sites over expanding.