1) The different texture is most the result of how the tree grows. There's soft grain and hard grain. The softer areas wear faster whereas the harder areas don't. This results in the softer wood leaving "valleys' and the harder wood being 'peaks'. When you say "where the grain shows" I'm assuming you're referring to the softer grain, and that you're using a water base product.
If you're using a water base finish, the softer grain will absorb more than the harder grained areas. When wood absorbs water/water base (wb) finishes it produces fine "hairs" that stick up when it dries. Your valleys in the softer grain also allow more finish to collect, making them shinier/glossier than the hard grained wood.
To eliminate some of these 'hairs' you can do a couple things:
- pre-wet the floor, let it dry and sand with a fine grit paper.
- dilute the 1st coat of finish (about 10 -15%) with water, then following directions on can, (within the recoat time) apply a 2nd, undiluted coat. Let this dry overnight
- next day sand all surfaces with a fine paper. Vacuum up dust, let room sit for an hour or two for any dust to settle, and apply your final coat
2) Regular furniture finishes aren't a good idea for floors. Floor finishes come in a variety of sheens, but also have some non-skid additives that prevent floors from becoming too slick - even if a satin finish. They're available on-line or at a professional paint or floor supply store in your area. Some good floor finishes are:
Bon Ami https://us.bona.com/