Have you thought this through? If your birds start to produce babies, do you have homes for 8 to 15 babies a year? Are you set up to handfeed the babies (syringes, pipettes, formula, incubator) if the parents won't feed them? That usually means anything from getting up every 2 hours around the clock for the human parent to staying home for the first month of their lives, or taking them to work with you while you handfeed and raise them.
Surprisingly, many cockatiels have NO idea of how to raise babies, at least the first round. Or, they may decide to mutilate the babies, forcing you to pull them for handfeeding.
As you have already found out, hens lay eggs quite well without them being fertilized by a male. The eggs that she has laid will not hatch, even if she does decide to try incubating them. Biology of laying eggs does not have a lot to do with the bird having any desire to be a mother -- the number of hens who eat their own eggs, fail to incubate, or shun their hatchlings to die of cold and starvation indicates that there isn't a whole lot of an emotional desire to reproduce so much as a hormonal urge.
Will they mate straight away? Unpredictable. Usually bonding and courting will take place for weeks ahead of the laying of eggs. Some hens are very promiscuous and will mate immediately with any male that is capable -- or offer up to a favoured toy, or human for breeding. It is entirely possible that the mate she has already selected is a member of the human family, and that she is going to see this new male as an interloper (especially if she hasn't seen others of her kind in 5 years).
Add to that that any new bird brought into the flock needs to be in quarantine away from your existing bird for 30-120 days to see if he is harboring any diseases that the stress of a new home will bring on. I ignored that principal one time and ended up with the entire flock having to undergo testing for psittacosis and spending hundreds of dollars.
Basically, this breeding round is out. A year old male may be physically capable of fertilizing the hen, but he is much less likely to prove to be an adequate father with sharing incubating chores. He also needs to be quarantined, so that interferes with any introductions at this time.
Does your hen show any interest in the eggs? Is she acting 'dragonish', flaring her tail, puffing her feathers, opening her beak to bite your hand, rocking back and forth over top of the eggs? If so, it is better to leave the eggs and let her get bored with the whole process. If she shows no interest,then you may remove them, but if she is getting broody, taking the eggs away will only inspire her to lay more eggs to replace thelost ones.
Cockatiels also are cavity nesters. Not providing a proper nest box usually causes stress to the bird(s) and frequently results in a failure of the nest and babies (i.e. death).
My recommendation at this point -- quarantine the male in a room away from the female to prevent the spread of possible disease. A well-bird exam by an avian vet would also be in order for him.
When the two birds are introduced, you will need a neutral area that neither has established as their own territory (the cage she has been living in is HER territory and she may not take to letting an interloper anywhere near it). A non-territorial area like a play gym is a good place for this. And once he has a clean bill of health, you can start moving the cages closer together gradually and see how things go from there.
It is possible that she may never accept the male as a mate, especially if she is very bonded to a human. There has been a lot of poultrification of parrots in recent years to produce them the way one would a chicken, but being parrots, they still do retain parrot characteristics in selecting mates. That is, they will not mate with a bird that they don't like. On the whole, cockatiels are so severely hormonal that they are usually fairly free breeders, but hens can be choosy about their mates.
The time between now and the next opportunity for breeding you will need to do a LOT of reading to prepare if you still want to attempt breeding. Start with these;
Cockatiels! Pets - Breeding - Showing, by Nancy A. Reed
Keeping & Breeding Cockatiels, A Complete Guide, by Dulcie & Freddie Cooke
Cockatiels, Their Care, Feeding and Breeding, by Robert G. Black
The Complete Cockatiel, by Dr. Matthew M. Vriends
http://www.cockatiels.org/articles/breeding/breeding.html
http://www.cockatielcottage.net/feeding.html
http://www.cockatiel.org/articles/handfeeding.html
http://www.birdsnways.com/wisdom/
http://www.birdsnways.com/birds/artspctl.htm#Cockatiels
http://www.birdsnways.com/birds/artbreed.htm
