First question: There is no difference between "like to play" and "like playing." Some other verbs like this are begin, love, and prefer. It doesn't matter if you use the "to +VERB" or the "VERBing" form. I'm not sure about your second question. Do you mean "When can I use an auxiliary verb when it isn't in a question?" You can make a statement and use "do/does" when you want to stress (emphasize) an important point, especially if the person you are talking with doesn't have the correct information. "Fred doesn't speak Chinese, so he can't help us translate this." "Fred DOES speak Chinese. He's quite good at it." This means the same as "Fred speaks Chinese", but you stress the "does" to show that the other person does not have the correct facts / information. Same thing in past: Teacher: "Why didn't you finish your homework?" Student: "I DID finish it. It's one your desk." (This is the same as "I finished it" but it shows that the teacher has the wrong idea and you are explaining the correct situation. Don't write the auxiliary in capital letters like I did. : ) Don't use -s form for both does and the main verb.

i like playing football تحبى ممارسة الشى بشكل عام i like to play football تحبى ممارسة الشى بشكل خاص يعنى المشكلة كلها انك لو بتفضليها بشكل خاص استعملى التانية مثال انا بحب القراءة i like reading انا بحب قراءة القصص i like to read stories.

BRSwartz's answer is correct and complete, and I would have interpreted the second part of the question is the same manner.

like doing means you prefer like to do means used to do or habit