While cutting a watermelon, one may remove the seeds by shaking out each slice. Any seeds that remain may be removed by hand or with a knife, because that is the normal way to eat watermelon. This is on condition that it is done for immediate consumption. Le-khatĥila one should remove the seeds with some type of shinui (Ben Ish Ĥai, Year 2, Beshalaĥ 7). Some are stringent and require that one place the piece of watermelon into one’s mouth and remove the seeds from there (Ĥazon Ish 54:1), but in practice most poskim maintain that the seeds may be removed before the watermelon is placed into the mouth, because that is the normal way of eating.
If a fruit bowl contains a mix of good fruit and fruit that has begun to rot, one may remove all of the fruit that one wishes to eat or to serve guests at the upcoming meal (MB 319:7). If he does not intend to eat all the good fruit now, but is worried that the rotten fruit will cause the good fruit in the bowl to rot, he can spread out all the fruits so that they are no longer touching one another, but he may not separate the good fruit and bad fruit into separate piles.
When dealing with a partially rotten fruit, the point where the rotten part touches the good part is considered a mixture. Therefore, cutting off the rotten bit is forbidden, because that would constitute removing psolet from okhel. The solution is to cut out some of the good part together with the rotten part.