I understand your frustration, and while it may seem like gi has invented new ways to get us to pay them, they've actually given us a lot of ways to keep playing for free. You just have to know how to find them. While buying diamonds and/or paying the snatchin merchant are the fastest and easiest ways to get through quests (and there are plenty of people willing to do that, so why should gi not benefit from them?), there are still plenty of ways to get through them for free.
Someone might have already posted something like this somewhere before, so I apologize if this is redundant information. Also, there's probably a better place for this in the site, so moderators feel free to move it.
The answer to the riddle is in the achievements. Almost every final reward for level five completion is a grand chest. There are detective's chests which give 500 copies of all paid rooms (minus selene, mars, saturn, and boss rooms), collector's chests which give 50 copies of every charger in the game (minus mystic living room collections), snatchins chests which give a couple hundred weapons to banish snatchins, van helsing weapons chests which give 150 copies of all weapons to banish full moon monsters, and STEWARDS chests which give 150 copies of all boss keys.
The stewards chest is the key to getting through quests requiring you to enter boss rooms. There are still some achievements that I have not gotten to level 5 yet, but I know for certain that there are two of these chests out there and one of them is very easy to get. You get it from exploring the animatorium 100 times. I know, that doesn't sound easy, but I assure you that it is.
Step one is to build up your supply of plasma balls to search the room. Easily done from the mystic chests. Then, charge the warriors of resistance collection. Those items drop from the snatchin partisan and snatchin resistance fighter in the yard, or ask for them from friends. Pauline and sablesrgreat, you are both my friends in the manor, and I'm happy to gift them to you. Next, start or join an animatorium battle. It's one of the cheapest battles out there, so that's helpful. Then, explore the room as much as you can in the two hour time limit. If you're really good, you can do the hundred in one sitting. After completing the achievement, you'll get your stewards chest and a bunch of gloriously free boss keys.
If battling is not your cup of tea, then just save those boss keys back for when you need them for quests. Each time, you go into a new boss room, though, plan ahead to try to explore it the 100 times, so you can get the other chests.
Here's another tip. While you're exploring all that time in the yard, your manor will fill up with phenomena. As far as I can tell, it's the easiest way to draw phenomena in. Make sure before you start your adventure in the yard that you have at least one of the phenomena that you want in your manor (two is better). By the time you're done exploring the 100 times, you should have phenomena all over the place. This is a good way to get through the blueprint quests.
As for selenoid and martian shards, gi has improved the drop rate from aliens in this last update. Also there are several collections to charge for them. Court your high level friends! They were once at lower levels too, and they remember what it was like. Most of them are extremely generous. You just have to ask. Look at what collections they charge the most (usually something that gives them bombs, flares, compasses, etc.) and gift them what you can. Again, though, mystic chests are a fabulous way to build those keys up as well.
As you can tell, I'm a big fan of the mystic chests. Honestly, they are the greatest gift gi has given players, since the olympic quests of summer 2012. Here's hoping they come up with something fabulous for winter 2014!
The other achievements that are easily done are: charging collections, using tools (throw a snail every time you explore a room until you've completed it), banishing snatchins, gypsies, robots, aliens, and full moon monsters (full moon is much easier once you've received a van helsings weapons chest, which is the reward for searching the crypt 100 times), and screenshots to facebook/twitter (set up dummy accounts so you don't annoy your friends, you can complete those achievements in less than half an hour!).
Anyway, I hope this helps you and that you might rediscover your joy in the manor. We've been losing players steadily for awhile now, and it makes me sad.
- shenanigans