How can the army ensure that their soldiers are actually reliable in a
fight, i.e. that they stay in the fight, that they know how to handle
their equipment, and that they're killing enough aliens?
In short...you can't.
If five hundred years have passed since the last war there are several problems you are going to face and I think the premise of the question is flawed in a couple ways. (that's not to say the question is bad, if I didn't like it I wouldn't bother answering)
- Military funding during peace time. Resources are focused where they are most needed. This would be especially true in a planet spanning empire. Running that large a government would be very resource intensive. If there is nothing to be gained by supporting a standing military force it won't be funded. At best a shell of command and specialists would be available when hostilities break out with aliens.
The US military is arguably the best in the world...and generally (Vietnam excluded) has enjoyed popular support. (if you want to argue ping me in chat)
With that in mind here is a chart of defense spending for the US military in the 20th Century:
Clearly during peacetime spending drops rather drastically, it did so especially during the era of total wars, which is the type of war it sounds like you are planning for. While well trained and experienced today, even the US military is not trained/manned/equipped for a total war.
Your planetary government would not support a standing military, let alone a large well trained military during peace-time. So experience is a problem yes, but having a large standing force trained in the basics is also implausible.
The second issue is military technology. Again, with no driver for development for over half a millenia odds are things have not progressed significantly. Perhaps technology has but its application for war and proven effectiveness just wouldn't be there.
So...how are we going to fare against these aliens. Poorly, especially at first. The first few years (if the aliens take that long to fight us) are going to be very...very bad. It takes a lot of time to develop a military infrastructure. Factories have to be built, bases have to be built, people have to be recruited and trained, weapons have to be mass produced...and keep in mind this isn't the middle ages, you can't just hand a guy a spear and say "Pointy end goes that way"
Training pilots takes 3-5 years, advanced weapons systems can take months, tanks take a while as well.
The inclusion of ancestral guidance would be helpful in training and operations. If nothing else it provides a baseline and can help in the creation of training programs, but if tech advanced over five hundred years you are starting from scratch on weapons training.