Heheheh.

Yeah, the combat is not so nice to new players. Lemme see what I can come up with to help you...
While you're poor on resources, the best thing to do is get your flagship outfitted with all the propulsion modules and
stay away from fights as much as possible. These modules are pretty cheap relative to everything else.
Do spaceship engines effect hyperspace travel so I can outrun Ilwrath patrols when going to meet Pkunk?
YES. Thruster Modules and Turn Jets are super important.
If combat is really doing you in, you can save your game before every fight and keep taking tries at it.
Avoiding Ilwrath: You don't need to fight these. They stay in their corner of space and tend to be pretty avoidable throughout the game. They even move sluggishly when travelling through their own space. So you could just save your game before travelling through Ilwrath space and loading if you get caught. Or use a retreat sequence to run away from them, since they're fairly slow-moving during combat too.
Fighting ilwrath: You want a flagship with a Fusion Blaster (this is the first tech upgrade the Melnorme will sell you), three Dynamos, and a lot of crew. All you have to do is move towards them and unload when you think you're lined up with their ship. This loadout for the flagship is way stronger than an Avenger and can pummel them in a head-to-head shoot-out.
Fighting Probes: Again, the easy way to blow through these is with a Fusion Blaster. Or rather, two of them, one in front and one in the second-from-front slot. Slylandro Probes are dodgey and the three-directional attack that two Blasters gives you is great at catching them even if you can't line your shots up very well. Spathi ships are also good for this fight, though that takes some patience.
The ally species you're looking for is the
Orz, whose ships can beat pretty much anything in adventure mode in a 1-on-1 fight. With this ship, you can pretty much win fights by flying away from your opponent and holding down both attack buttons to spam space marines. The marines will zoom over to the enemy ship, jump on board, and smash everything to pieces. The only catch is that your Orz ships often run out of crew, so you often want to
retreat your Orz during a victory ditty by pressing Esc.
Fighting Ur-Quan: Spathi can beat these, believe it or not (the Spathi ship is actually quite badass in general). It takes some skill, but if you mostly focus on dodging and just keep dumping torpedoes from medium range, you can beat these guys. There's a second... type of Ur-Quan that's also beatable with Spathi. Orz are more fool-proof than Spathi, and the flagship can do the job too if you've upgraded it enough.
Is there a way to make combat easier?
Get all the Melnorme tech upgrades and turn your flagship into a doomsday machine. Hellbore Cannons, Tracking Modules, Shiva Furnaces = long range homing attacks that wipe out anything effortlessly.