How to preserve fresh picked tree branches/leaves and flowers? ?

I really don’t know if it can preserve flowers but i see my older sister did this.

she iron the flower in between wax papers (just lay it flat ) so you can make bookmarks and stuff (once it dry you can laminate it)

or sometimes she insert in between a very large book(i don’t know if it works) =>

It depends on the bloom.
Roses you hang upside down ( to keep the stem from bedning over at the flowerhead ) for about 10 days and let them air dry. This is best done with buds or roses that are completely open. The older the bloom the greater likelihood you will lose the petals.
Same for Hydrangeas as far as air drying.

You can also try using parrafin wax on rose blooms. I’ve never tried it myself but I’ve seen it done and looks nice. Melt the parrafin in a double boiler and quickly immerse the bloom in the melted wax. Don’t leave it in there for long or it will wilt. Stand the blooms in a piece of styrofoam to dry.

Other blooms are better pressed as air drying will only leave them looking ugly.
Petunias and Pansies. for example press beautifully but shrivel up when air dried. Daisies press beautifully, too.
To press them put the blooms between two sheets of paper towel or blotter paper and place them between two heavy books. Leave them undisturbed for 10-14 days. You can frame the pressed blooms or use them to decorate cards, etc.

Blooms like Mums and Carnations don’t dry well. They are too thick to press nicely and they just look dry and bedraggled when air dried.