I have an indoor lime tree and it grew blooms and fruit for the first time (in seven years) this spring. I'm very excited. Now, it has 4 or 5 fruits on it and they've been on there since April or so. I read that I need to wait until they start changing their color to slightly lighter green, but before they turn yellow, before I pick them, but they've been on that tree for so long and it's winter again. Should I just wait or pick them now while they're still green?
Citrus typically takes a long time to ripen. Valencia oranges, for example, will still be completing the ripening process even after the tree has flowered and set fruit for the next season.
You did not specify what type of limes you have. Key limes are typically shorter (three to four months in ideal conditions) but can take longer depending on lighting and other conditions. My outdoor lemons in zone 9b would flower in March and be ready in late December to January. I suspect you're getting close to harvest for your limes. Ripe limes should give a little bit when gently squeezed. They should not feel firm or completely solid.
Do not harvest everything at one time until you've determined they're acceptable to you. Pick one and see if it's to your liking. It should be juicy and tart. If it's not juicy, it's likely under-ripe.