(Hey! I've been looking into getting into more "professional" (?) rp on tumblr. Stuff like you are doing! Do you have any tips and tricks? I'm on computer btw. Have a great, wonderful, outstanding, and even better, day/night!)
Sorry I took so long but I wanted to give you the best answer possible to this question. I gave it some thinking as well.
First off, thank you for calling me a 'professional' rper! I have no idea I even fit into that category, as this is just for fun and comes second to my actual writing for my original content. I take that as a huge compliment.
I can tell you some things I do, that may help you.
I always try to come up with an in depth, rp or I try to make one from whatever plot I'm doing. Having an interesting plot that both you and your rp partner will be invest in is something that I feel is a must. It's like living your own adventure where you can make your wildest dreams canon! I like to think of the possibilities, the what-if's of any situation and it makes for good exploration of headcanons as well.
I always try to establish a scenery especially if I'm writing starters. The setting is very important and your partner needs to know where the hell these characters are, if not they just seem to be floating in the void. Atmosphere is everything and it can establish a good tone for your roleplays and help convey to people who read them what they should be feeling (i.e.if you use descriptors relating to the state of buildings around them, the colors you might want to portray, the state of the sky and luminosity of light sources you can convey an overall mood - something with less light source will give off an eerie or gloomy mood, and something with a lot of light source will be precieved as cheery).
When I rp I tend to think about how characters feel, the presence they give and how my character would feel in relation to them. I even think about how my own character would look and feel in a real world setting. It's immersive and can establish fun interactions to characters who haven't encountered anyone like them before. Thinking about how a character moves, their posture, their bodily movements, their clothes and textures is important.
I also think about how it would feel being in a certain place. i.e. Dark World seems cold due to the lack of light, so I imagine the air would be chilly or even freezing in certain areas. Atmosphere and how it makes you feel, exploring the senses will also give immersion to your rps. A character's feelings are very important.
Also I feel if your character has a story to tell than it's best to draw it out, let your rp partner get to know your character and bond with them before you do anything gut-punching. We all want those twists, those tragic backstories but be mindful that presenting one too soon will make someone care less. If a random Joe walked up to you on the street and told you his wife and kids died in a fire, you'll feel bad, sure but you don't know him. This might sound mean but it's just how people operate. Now, if your best friend whom you've known for years approached you and told you this, you would be more inclined to express sympathy or maybe even cry because this person impacted you. You got to know this person and you feel that attachment. Characters function in the same way.
Sometimes you do have to work for that plot, that gut buster of a backstory, but it's worth it to get the response you desire instead of a half-hearted instant gratification.
Also, looking up words will expand your vocabulary and make your writing better if you feel you lack something or you use certain words too much. Searching for synonyms is something that I do a lot when I feel my writing is not to my liking and you learn a lot of new words to use too.
If you are creating an oc, make sure that everything you make about them makes sense. If you have to, write out notes. You don't want to contradict yourself because you just might get called out on it or asked in the rp why your character feels x for this situation but x for another similar situation. Giving characters fluidity is very important.
The last thing is, if you're going to make a character have a mental illness or you headcanon a canon character with it, please do research on that illness. If you have to, go to youtube and watch someone's videos who does have that illness and see how they battle it, what they have to say about it and how it makes them feel. There are a lot of good channels that talk about mental illnesses and people who share their experiences. Getting a personal account of it may help you on whether or not you think your muse has said illness or set of illnesses. Sometimes, you may make a mistake in how you precieve someone with that illness and when you put that into your character you may inadvertently come off as offensive to someone who does have it. As a mentally ill person who roleplays, I can say it's happened to me a few times. Besides, you may be doing it to try and break stereotypes about said illness so you definitely don't want to put something out there won't empower people or have them see your muse as so much more.
Researching anything about your character will always give you cool ideas, like language barriers, cultural barriers, how they may or may not think about characters who aren't what they are and you can even build upon things like powers in battle and their overall make-up. What things will effect them, what will not and so fourth.
I hope this very long-winded answer helps you and anyone else who aspires to take their writing to another level. I hope that you have an outstanding day/night as well anon!