Can you make money in the stock market buying and selling the same stock?

Yes of course. If you sell when you've made more than your brokerage (buy & sell) you win, and of course you can't (generally) sell that which you haven't bought first. Timing the market is literally how speculation works. But consider that you need to ask yourself

a) So when should I sell? (obviously when it's lower than you bought)

b) Is there any more money on the table (will it go up or down from here)

c) Will it go up or down after you sell some? (should I buy more soon, leave it to go down more, or just sell the lot)

So basically you need to guess the market or do tons of research that might back up your hunch on timing.

If anyone knew the market in the future this would be a lot easier! Of course nobody does know so it's going to involve an element of risk and your reward will be the inverse of that in an efficient market.

I would say though, focusing on a small number of stocks may increase your likelihood of your research working for you as you become sensitive to things that matter to a specific stock, but you won't be alone in that. Now having said that, you may get great at watching and working a 5% swing in a particular stock but missing the opportunity of a 10% growth elsewhere.

If you're a beginner, you're as likely to lose money rather than make it so I'd go with a long term buy & hold on an ETF where the fund is something you believe in. But that's not an answer to your question.