Title: Are there any mistakes? [Do not use "a" with a plural.] Do not space before a comma. The word "with" is optional. Place the "but" at the beginning of the clause.

..... I've painted the background (with) blue, and the flowers (with) red. I haven't started yet, but I've been planning to read "Anna Karenina." "with blue" and "with red" imply you used other colors too to paint the background and flowers. If the background is entirely blue, and flowers (at least the petals) entirely red, you don't need the word "with".

'Are there any mistakes' I’ve been drawing for a week. I’ve painted the background (in) blue and the flowers (in) red .I haven’t started yet , but I'm planning to read “Anna Karenina”.

Overall, you don't want to start all of the sentences in a paragraph with the same word, particularly a contraction. There are too many "I've"'s in this paragraph. This has to do more so with the sound rather than the grammar however. The grammatical problem is in the last sentence. Here is it corrected: I have not yet started reading "Anna Karenina," but I have been planning on reading it soon. Note that in your sentence you use two contraction in a row I've haven't this is incorrect because it means: I have have not Try to remember what the words in a contraction are Keep working at it! Good effort :)

are there any mistakes? (we use 'a' for plural only few cases like a lot of mistakes.) I’ve been drawing for a week.I (here have can be used, but even without have it gives the same meaning) painted the background with (with is optional here, it is preferred like when you mention more than 1 colour like white with red, even now it gives the same meaning ) blue and the flowers with red .I haven’t started yet , I've but (here you have to remove "but or I've" ) been planning to read “Anna Karenina”.