Trench coats were originally designed for soldiers as a top layer. They are worn to protect you from weather conditions such as rain or wind, not necessarily to keep you warm. If you want to be able to button your trench coat, you can still wear layers underneath but not several thick layers.
Usually, the bottom button is left unbuttoned. Today, the reason to leave the bottom button is different than where it originated from. It was more practical to leave the bottom button unbuttoned because the men who wore them rode horses. Leaving the bottom button on your trench coat unbuttoned allows for more freedom of movement.
Trench coats go with a lot more than you would think. They match well with a floral dress or skirt that is longer than the bottom of your coat. It doesn't have to be longer than your dress or skirt though.
As for styling a trench coat with jeans, straight leg or skinny jeans are preferred. This is because the slimmer jeans balance out the flow and shape of a trench coat.
Last but not least, you can style your trench coat by adding accessories to match it. For instance, you can sport a wristlet wallet or a small cross-body purse. You can add a scarf for a pop of color to dress it up a bit.