You can do all these things on your own but of course you have to research it and if you want to visit Masaya and Lake Apoyo in one day you really have to figure out how to get from one to the other. We went to Catarina and the lake as a day trip from Granada. And we actually stayed overnight in Masaya but we had the time to do that. If you want to do it on your own, it would be be best to take a bus to Managua, get off at the Masaya volcano, after the visit flag down a bus going to Masaya, hopefully there find a bus going down to the lake (I think there are only 2 a day though) or a bus going to the entrance of the lake and walk from there or get a ride there or a bus to Catarina (for the viewpoint) and take a taxi from there. Or take a taxi to the lake from Masaya (it is not far). To Lake Apoyo from Granada you can take a bus to Niquinohomo and get off in Catarina and then take a taxi down to the lake. There are hostels in Granada (Oasis for example) that have shuttles to the lake. If that all seems like too much work you can go with a tour (check the tour operators in Granada, for example : http://www.juliotoursnicaragua.com.ni/index.php/full-day-tours/61-laguna-apoyo-and-masaya-volcano Or go to the central park and negotiate with one of the taxi drivers. For $60 he will take you around for the day and certainly Masaya and Lake Apoyo are possible in a day. Of course chances are he won't speak much English, if at all, so take a phrase book, learn a few basic phrases and it will go just fine. All you really need is agree on a price and have the destinations written down. But just a bit of Spanish goes a long way and will make your trip more enjoyable. Or ask your hotel for a driver for the day.
As for Ometepe. This is the bus schedule : http://www.ometepenicaragua.com/ometepebus.php
You can figure it all out yourself. We did. We have taken the bus, walked, taken taxis and even hitchhiked. Again, you can also negotiate with a taxi to show you the island. Or you can rent a scooter/motorbike. Or your hotel can help out. They can arrange all the activities for you including transport. You can contact the horseback riding and kayaking place and figure something out. Just decide on what you would like to do when, the best order and look at the buses, get a taxi, ask your hotel, walk or a combination. For the horseback riding, kayaking, the waterfall... base yourself in Merida or Santa Cruz. From there Ojo de Agua is not too far. Visit Charco Verde on the way there from Moyogalpa or on the way back.