i love push ups and im doing (5-6) push ups at this moment and increasing the amount every session, but as i heard about rest days i want to know what exercises are ok to do during rest days? Actually im not intrested in gym yet and i want some relatively easy to perform home exercises thankyou :)
If you want to let your "pushup muscles" rest, that's good.
I would suggest throwing in pullups and squats, either on the same day as you do pushups, or on the days in between.
This way, you're not only training chest/triceps, but also working upper back, biceps, and legs.
There are a million different bodyweight exercises you can do with minimal equipment. I would suggest trying to find a good number, so you can have some variation in your training.
In addition to Alecs good answer and the comments I wanted to add, that there a a lot of different dodyweight trainings availible today. Starting with different polpular Books like
Mark Lauren - You are your own gym https://www.marklauren.com/
or perhaps in your case better: Paul wade - Convict conditioning http://www.dragondoor.com/b41/
which are delivering a huge amount of knwoledge and how to increase your strength and "health" without a gym/equipment. (Also there are autors like Ross Enamait, Pavel Tsatsouline, Kelly Starrett... just to not only give you two names and countless forums and homepages online, google hundred push ups program).
Especially Paul Wade has a program to increase your ability to do push ups, pull ups, squats and leg raises from the very basic in Step one to extreme hard (one arm variants) in the last Step. Just have a look into one of those to better plan your training/extend your knowledge.
Now back to your first question. The needed rest in between workouts depents strongly on the amount of excercise you have and you perform as well as genetics. There are athlethes who can train several times a day without the need of a specific rest and others who have to plan their training very carefully to not overtrain/get enough rest. To be honest, just try whats goof for you. If you can perform push ups every day, do so (while at best mix in some other exercises to train the whole body). If you feel sluggish or you feel pain while trining stop and increase your rest. Try to listen to your body. He knost most of the time what's good for him.