Just some thoughts:
On small and crowded maps,Abysia is able to compete with the other nations even with bad research,because you can field nice armies via Blood Magic without the need to research a lot in this area.Every Demonbred is able to summon a Devil per turn for example.Of course you have to play very aggressively and maybe with a 9er Fire or Earth Blessing (for Lava Warriors) to get strong armies very fast.I have had great success with a Magic Scale of 0 in this type of games.
On big games,research is without a doubt very important.
Of course its all a matter of prefered playing style,but IMO you have to find a tactic with Abyisa that allows for a very good early expansion AND strong scales(Order 3/Productivity 3/Magic at least 2).
The first turns ,I always build Warlock Apprentices and all Heavy Infantries I can afford with the help of alchemzing the Fire Gems.If I have money left,I build a Demonbred instead of the Warlock Apprentices until I have 2 to search the newly conquered provinces immideately for Fire/Holy/Blood Sites.Afterwards I build the expensive Warlocks to get some important random picks,like 3 Astral,4 Blood or 1 Earth(to be able to summon Demon knights with help of Blood Stone).
I always make sure to produce a capital only mage every turn,If you cant do it,you did something wrong,mostly that means you did expand too slow or you didnt concentrate your efforts on the income rich provinces
I find conquering Indie provinces with Abyisa quite easy.
A bunch of Heavy Infantries+your starting Infantries+Anathemant Salamander(for Fanatism/Flare)+ a Pretender that is able to cast Flare will conquer most provinces with few,if any,losses.
Strong Crossbowmen provinces I leave for Slayers to assassinate the leaders,which I produce as soon as I have a second castle,and scouts to take afterwards.
Strong Knight Provinces I leave,until I can use my 1-2 Demonbreds also for battle ,i.e.until I have researched Fireball.
Research Construction 4 first.Afterwards Evocation for Fireball and then Blood.
Fireball is quite important for my playing style regarding initial expansion.
If there is a very strong indie province,I can use Demonbreds to cast several Fireballs and thus to support my army.Fireball causes much less Fatigue and as such is the better spell for Fire 2 and also Fire 3 Mages than Flare.
Because your mages have very bad precision,I prefer to be able to cast 4-5 times Fireball with every mage per Battle than 2 times Flare with Anathemants only.
Generally,as soon as I have 2 armies going,a second castle and a Slayer pack(effectively resulting in 3 armies that can conquer indie provinces) i send 2 aprrentices on blood hunt to get slaves for dousing rods.
Now that you begin building up a blood economy(depending on the strength of your surrounding indie provinces and income they give you,this is always doable by turn 10-15) you desperately need another province to produce mages for research.
If you dont have at least 1 library yet,search for magic sites more deeply,with 1 or 2 warlocks,preferable with Nature or Earth random pick, and 2 demonbreds.Sometimes you find a site which gives you indie mages.If you still have bad luck,prepare to attack one of your human neighbours.
Its a simple thought:If I cant compete in research ,I need more provinces/Income/gems than the research strong nations to be able to compete.
As soon as I get good research up,I try to make peace and concentrate on higher Blood magic summons.At this time I only produce mages,no normal troops anymore.
My prefered Pretender for this is a Scorpion King with 4Fire/4 Earth.
He is an ok battle mage right from the start via Flare and later Legions of Steel+the ideal magic site searcher for the start especially in mountain provinces.
Also he can produce some items for you to get your Earth 1 random Warlocks to produce Dwarfen hammers.Later he can forge Elemental armors for you and can cast some good ritual spells with help of magic boosting items.
I rarely build him up as an SC,because as a blood nation you normally can field lots of strong other SC`s.