How can I answer inference questions for reading passages without just guessing or using my 'gut feeling'?
I like to think of inference questions as a mystery and you're the detective that needs to find the clues. Use clues in reading passages by identifying transition words, positive/negative connotative words, and key words to eliminate incorrect answers. Practice inference questions through answer justification: Why is this answer right? Why are the other answers wrong?
How can I increase my speed and accuracy when playing piano?
Scales! Spending at least 15 minutes every day running through scales (major and minor, multiple octaves, arpeggios, etc.) can greatly improve the dexterity in your fingers to allow you to play with greater speed and accuracy.
How can I improve my speaking skills if I don't have anyone to practice with?
One of the best things to do is get some kind of recording device and record yourself speaking, then play it back afterwards and critique yourself, paying specific attention to pronunciation, fluency, and coherency. Another great way to improve pronunciation and fluency is by watching movies, TV shows, or Youtube videos or listening to podcasts in English and focus on imitating the pronunciation and style of speaking.