Only remove the suckers to start. Then after the first cluster of flowers sets tomatoes you can remove the leaves below that cluster. I typically wait for them to start yellowing because at that point they are useless. Continue this as your fruit ripens. If sun scald is a concern you can let a few suckers grow to shade the fruits then top those making sure not to let flowers form. As for ferts I'd use a liquid like TTF or something similar.
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