I have two resident cats, and I frequently do short-term fostering for a local rescue, so I have to do this on a regular basis.
You’ve probably already read the advice I’m going to give, but start slow. Put the new cat in her own room for a while. Make sure you can keep the door closed. Your resident cats will know she’s there, and will sniff around the door and try to sneak in with you, so be careful.
Start introducing them through smell. Mina will probably already be surrounded by the resident cats’ smells, but you want to give them something that smells like her - a blanket that she’s been sleeping on, or if she’ll let you pet her already, you can rub a couple of socks over her (especially her face) and then give them to your cats to investigate. If they react well, give them treats. You can also start feeding them near the door to her room so that they associate her smell with food. Some pages would recommend feeding her near the door, too, but I find that new cats are a little too scared to eat properly anyway so it’s better to put their food in a spot that will feel safest to them.
Next step is to get them to swap rooms. This can be tricky because you don’t want them encountering each other when you do this. If you can, get the resident cats in one room and shut the door, then let Mina out to roam the house, and when she’s safely in another room, put your cats in the ones she’s been staying in and shut them in for a while. Let them do all the sniffing around they need to do.
If you can, then it’s good to let them see each other without being able to touch. I have glass doors in my apartment that they can watch each other through; other people do this with crates.
When they’re finally ready to meet, watch them very carefully and don’t leave them alone together when you’re not there to supervise. A bit of hissing and growling is normal, just separate them if it goes on too long or if any of the cats is clearly in distress. Again, reward them with treats for positive interactions.
How long all of this will take depends on the cats in question. I’ve never had to spend longer than a week at it, but I’ve heard other people say it can take months. If things seem to be going badly, you can always start over.
Oh, and get Mina spayed as soon as possible.
Now let’s see those pics 