UFOs: UFOs come by every 3 or 4 hours. They are random and will provide random prizes. If you get the UFO with a prize that seems of low value and you have time, don't click on it! You can refresh the page or just click another link to go to another part of the game and wait until you get another UFO. They will reappear if you don't click on them at that time. If you keep missing them, they'll keep reappearing at random intervals (sometimes a long while though) when you click on a new page, so there's not a risk of actually losing them. There is a risk of losing them if you're not actively on for a long periods of time though, so at the point you may want to cut your losses and just click on what it gives you. For example, if you see a Mash, you will only get 1 Mash from that UFO. So instead of clicking on that Mash UFO, you can click around the game pages and wait until you get a better prize like the 3* Saddle or Aging Points. That way, if you didn't need that saddle, you could always sell your 3* saddle at the store to get half back (so about 1,500 Equus as of today) and buy a lot more Mashes (at this time about 24 of them) with that instead of only getting 1 Mash. 
Getting congratulations: The easiest way to get congratulations is by congratulating other players first. People in game will usually try to congratulate back (I also do this, but I do admit I've been horrible at this lately 
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Xanthos: You are able to interact with Xanthos divines (even ones that belong to other players). You simply go to their page and on the action items, there will be an extra button with the apple button called "Stroke." If you do this, you can get a *chance* to get a Horn of Plenty (HOP) BMI. If you did win a HOP, you'll get a mail notification the next game day and it will tell you that you won a HOP. You can stroke 5 Xanthos' a day. Each Xanthos you stroke gets you a different chance. For example, if you stroke all 5 different Xanthos, you get 5 different chances at a HOP. I've once won 3 HOPs from the previous day's actions 
Frost: You are able to interact with Frost divines (even ones that belong to other players). You simply go to their page and on the action items, there will be an extra button with the apple button called "Defrost." If you do this, you can get a *chance* to get a Hypnos' Blanket (HB) BMI. After you press the button you will get a banner on the top of your page saying "You've just defrosted Frost!" or that you've Won a HB. You can defrost any 1 Frost a day. In addition, if you're SUPER lucky, you might even win a Frost divine! The only condition being that you have to defrost at least 1 Frost the last month in order to win in the next month. 
Topaz: You are able to interact with Topaz divines (even ones that belong to other players). You simply go to their page and on the action items, there will be an extra button with a sparkle button called "Congratulate." If you do press that, you can get a *chance* to receive 10 Passes! If you don't receive the passes, you STILL get 50 Equus! After you press the button you will get a banner on the top of your page saying "You have just congratulated this Topaz! Thanks to him, you have won ---!" You can congratulate up to 5 Topazs a day and each Topaz you congratulate gets you a different chance. 
Archimedes: You are able to interact with Archimedes divines (even ones that belong to other players). You simply go to their page and on the top of their page, you will see a box. In the box it will show you a question posed from other players and if you answer the questions correctly, you will always get 1 Aging Point. If you don't answer the question correctly, you'll get nothing. All answers to these questions can be found online and a some players just have the answers on their pages/EC pages/etc. 
E.C. Earning Equus: Even if you do NOT wish to run an E.C., it's a good idea to start one to simply make use of the farms. You can also just ensure no boarders by not having boxes or reserving all your boxes for your horses only. Making use of the farms gives you the Cows. These cows are incredibly lucrative. They produce "leather" that can be sold for 5 E a piece. Or if you want to further make more money, then use it to craft and sell the crafted items. It's best to go for the Longhorn cows even if they're more expensive up front because both cow options take the same amount of days (30), but the Longhorn cows produce significantly more leather. This way you're ensuring you're getting the most out of your cows and time. You also want to be using the Large meadows (25 acres) and putting Feed troughs on them for the same reason that they produce much more leather. Having all 3 conditions provide you 35,750 leather (178,750 Equus if you straight sold it for only 1 plot). If you have max (6) meadow plots with these cows and the same conditions, you'll be able to get 1,072,500 Equus every 30 days from these cows! In these use cases, fertility does NOT matter, and the Feed Trough does NOT decay. So that means you can infinitely keep doing this every 30 days and all you have to do is pay the small Equus fee for the Longhorn cows to keep growing them for that approximate 1 million per month. You'll easily get back your initial investments and much more! 
That being said, because they do take up a meadow space, you'll need to be careful if you wish to run an E.C. as it will prevent you from using those plots to grow anything (including pass seeds) until they are either finish growing or you remove them (which means the cows are completely gone, and you do NOT get reimbursed your original fees to pay for them and you lose all progress from them growing). Of course if you have several plots available (seen on your meadow page under "Number of crop fields and cow raising meadows x/x" then you could always figure out what you can allocate or not. And of course, you could always just buy the items you need for your E.C. from the Store instead of using meadows.