1) Gates are technically sort of two-way. The actual wormhole stargates produce is indeed two-way but it's too small for a human to fit through, however, energy signals (like teleportation beams) can travel both ways. It's just that when a gate connects, the teleporters built into the gate are set as an entrance and an exit. And well, the exit teleporter vaporises things trying to enter it. So you could get singals back. Additionally, it is possible to disguise the origin of a gate connection. This is difficult, and would be one of the major difficulties of this project even with The Toddler Test, but the Nox have been shown to be able to produce connections without the Dialling sequence or the energy wave using a bog standard gate - presumably this is an advanced control method that doesn't use the DHDs, but honestly we mainly see the SGC using those and they are absolutely terrible at R&D. Apophis also is implied to have done something similar in the first or second episode. As such, this project is mainly focused on improved gate understanding with a comparatively simpler design for the scout, probably a spirit of some kind. Honestly I think I might have underestimated the scale a little when I proposed it so it might end up running over if you do pick it.
2) This is intended to be a starter project to show what you are capable of to Ainsley and give him hope that you can create a fighting force capable of holding off the Hunt. A Hero Weapon may not seem much to something like us, but to the level of war that he's used to and the sort of war the Goa'uld regularly employs, powerful single units are extremely useful. The weapon in this case would likely be an upgrade to a Goa'uld staff weapon, or something along those lines, capable of piercing known examples of Goa'uld armour and allowing you to be mobile enough to dodge retalliation or withstand shots from a staff. Probably wouldn't be enough to stand up to aircraft, but it's the easiest of the tthree projects.
3) This is where me not explaining things too well bites me in the ass. You've heard of the Hunts before to get some idea of how things work but I didn't go into too much detail at the time because it felt superflous. That said, the Goa'uld use a slave army of Jaffa and arm them for terror more than battle. Staff weapons are fairly powerful, but have a rate of fire and accuracy more in line with a musket - that's their standard weapon. Beyond that they have intars (stunning weapons that they use for training) and Tok'Kals basically sci-fi stun grenades. There are stun guns (that also do disintigration) but those are generally limited to actual goa'uld.
They do have air support but it's mostly air-to-air fighters and a few bombers these wouldn't see much use in hunts simply because the weapons are too powerful and wouldn't be useful for taking slaves. Most of their land infrastructure is legitimately medieval outside of personal equipment, mainly because the Goa'uld fear jaffa rising up against them - something which has happened in the past.
Jaffa are humans with minor genetic modifications. The modifications generally mean close to peak human physiology (in a generalist sense, not in any particular field) but it is mainly there to remove their immune system and make them dependent on symbiotes - baby goa'uld - those symbiotes do grant them some additional strength and healing but it is relatively minor, they aren't bulletproof or anything. Their armour also does nothing to protect them from staff weapons, more from arrows, bolts, knifes and other tools primitive cultures may be able to access.
Hunts are also notably distinct from wars, they are slave-capturing and culling missions. Sure, some of it is to ensure that technology doesn't progress too far, but beyond that sort of scouting and elimination, Connaing and his forces don't expect a great deal of resistance.
