GrimMyfanwy

Sorry but you are wrong here. They don't need to be killed by heat for the shard to work, they just need to have the status on them. Increase Secondary Critical Chance by 1% (1.5%) every time you kill an enemy affected by  Heat Damage. Max 50%" even at a 20% status rate, with primed heated charge, she's guaranteed one proc in the 30 or so rounds per second she puts out. So even if they don't take a lot of heat damage due to shields or resistance, it will still activate. Also, Arcane Avenger only works if she takes health damage which with her low health and armor is a death sentence on SP even with Adaptability maxed out (if it's on your build). You could go with the combat discipline trick, but that ends up costing you 10 mod capacity from your build just to get an arcane working when the point of arcanes should be buffs that don't cost mod capacity a better suggestion would be Arcane velocity, which while not increasing your Crit Chance, ups your fire rate to insane proportions.
I tried out a 5 topaz build on my mesa, and even skipping the frankly overly tedious build I think DeckChairVonBananaCamel is referring to (it actually requires you to get 37 melee finisher kills at the start of a mission using an arcane that has a 5% drop chance and you only get 5 chances for it per week), it really does a lot more damage than my previous 5 red shard build. Worth the yellow shards IMO

For XP, for lower level AW's and AW wapons, running the two mobile defenses are very useful. The trick to remember is unlike regular warframe missions, AW does not seem to follow the xp division rules (25% to your WF, 75% to your equiped weapons) Instead it seems to split the reward between the AW and only the weapon used for the kill (Shared XP from other players' kills seems to be divided normally, I still need to do more research)

As far as mods are concerned I used to recommend earth interception for both leveling and mod farming, but now that that is no longer an option, my clan has found that corpus sabotage and grineer MD are the best bets for an underpowered AW for mod farming. 

If you are in a clan with the Itzal researched, I too recommend this as being a far superior AW to start with, besides the 3 power working like a super vacuum, the one allows for fast movement, 2 is great for farming mobs with an underpowered weapon to level it and 4 is great cover, letting you focus on kills while the fighter escort knocks out anything that gets too close.
 
Good luck.