Could use some tips, advice and suggestions for my primary load-out (Insanity difficulty)

Game still sort of new, and I haven't really used biotics on Ryder.

For crafting, there isn't too much to say. I have been using a mix of armor with Pathfinder chest and helmet, whatever arms, and now the Maverick legs, but I am playing more or less a soldier so that works for me. I like the Shield Fusion mod since it sort of works with a couple other passives and things that are based on low health.

For weapons, I like to use the Mod Slot or Double Mod Slot as one augmentation. There is an augmentation that will boost shields whenever you empty a clip, and another that will restore health every time you reload if you need it.

My main weapon loadout has been a Revenant and a Carnifex, and that might not translate all that well to biotics. The gun I actually had the most fun with was a Vanquisher III I picked up though. Now my crafted Valiant III is better, but doesn't have as good a feel for whatever reason.

I don't like the Carnifex's rate of fire all that much in this game, but it is ok with a scope to do some ranged damage, and you get the schematics as you level up.

I picked up a Hurricane this evening but haven't tried it out yet.

I went full on remnant (armor included) except for the asari sword. I love the PAW augmented with a bio converter for infinite firing and a Inferno as my combat sniper. Now for profiles i had three, first was soldier with turbocharge, invasion and barricade. Second was vanguard with charge nova and invasion for now and finally third was soldier again with concussive shot specced to power cells, flak cannon and omni grenades. Profile 3 was for when i needed to unload everything quickly at something, great for bosses etc if you have some cover.

now some tips:

1: Look at tech tree passives properly as they provide massive value. HP regen on demand which counters the bio converter perfectly, 30% more weapon damage, shield regen etc etc
2: get barrier passive from biotic tree
3: melee weapons augments like 3% weapon damage also apply to any other weapon you use as the melee weapon is always equipped. So a asari sword with 5 kinetic coils will provide permanent 15% weapon damage.
4: Barricade with shield delay evolution is literally a life saver and is a near must.
5: On havarl get the adrenaline fusion mod as it is one of the best and allows easier use of profile system since cooldowns stop being an issue.
6: DO NOT use augments that change a weapons firing behaviour, ie grenades electricity and that stuff. They will generally mess up your weapon.
7: Research the shield oscillator augment in the remnant tree and always put one in your chest piece. That coupled with power restore bonuses from tech tree means instead of just 25% you get close to 50% shield restore on kill and a bit more with vanguard profile if you have to get up close and personal.

Drack is shit against Architects. So is Cora probably. You need range to deal with them. Drack and Cora don't really have any.

Not biotic at all but what I do on Insanity:
Playstyle: Aerial bombardment then swooping in and mopping up the trash.

Skills & Profile: Flamethrower / Turbocharge / Flak Cannon spec for stun.  Combat Tools spec DR & melee, then eventually Combat Fitness & Team Support.  Soldier profile.  Flak stun and Combat Tools DR are probably the most important

Weapons & Gear: Falcon augmented with Plasma (non seeking).  Eagle secondary.  Shield Oscillator Chest augment; restores 20% shields on kill

Squadmates:  Not Vetra and not Peebee.  With Cora's Shield Boost, Cryo, & melee knockdown a Cora and Drack team is probably best for this mobile aggressive playstyle. 

Though Ryder is considerably less tanky than MP characters, has fewer consumables and cannot be revived, the Plasma Falcon does 2x its non augmented damage, explodes groups of mooks and can be made to be much more accurate than in multiplayer
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For Biotics you could replace Flamethrower with Annihilation Field speced for increased damage & lift field

^While on the subject, don't forget to grab the loot you get when you reprogram the Architect.

I am playing as the Sentinel as well. I'm about to begin my 'conversion' from 'just starting out' to badass. First, convert to the Explorer profile. Then research the Piranha shotgun. There is an augment you should have, can't remember the name atm, that converts your pellets into plasma projectiles. Use this, then all kinetic coils (you can buy these on the Nexus). The plasma augment eliminates the range issue with shotguns. There's also another augment that takes 5% of your health in exchange for no reload time. I personally prefer a sniper rifle (Isharay) and the Piranha, but you could sub the latter for the Hurricane pistol if you want. There's some augments that could do some crazy stuff with the highest rate of fire weapon in the game. Anyway, spec for weapon damage.

I use Shield Drain, Overload, and Throw atm. I will eventually move from Throw to Charge, once I get my Piranha fully RnD'd. The game in its current state is heavily weapon biased, but you must mix in some effective powers just in case you can't make it to a weapon box. Shield Drain will Tech combo off of Overload, even though there is no mention of it in the description. Always spec Tech powers vs. Shields/Synthetics. Armor isn't that big of a deal. I play on the difficulty just below insanity.

Armor, imo, is more of a personal preference. I'm not always worried about cover, not to mention enemies flank well, so the Remnant armor chest piece works well for me. If you find yourself always behind cover, then a different armor might be better for you.

Anyhoo, I would recommend a long range weapon and a short range weapon. There's not much in between. It's easy to kill from long range, as well as short-medium range with a good weapon. Killing from long range kills the fun (pun intended), but closing the distance with Charge and getting up close and personal then blowing their heads off with a good shotgun is highly satisfying.