Is current the same at all points in a circuit?

By Kirchoff's current law, the sum of the signed currents entering a node is zero.

In a parallel circuit, this means the sum of the (often single) current(s) entering a node (junction) is the same as the sum of the (two or more) currents leaving that node.

To determine the current in a particular branch, you need the voltage and resistance, or you need something else that you can use to calculate the current.

In the second case, if you know the total current and one branch current in a two branch circuit, you know the other branch by calculating total minus first branch.

For the first case, one method is to take advantage of Kirchoff's voltage law, which states that the signed sums of the voltage drops around a series circuit is zero. In a parallel circuit, this means that the voltage drop across each branch is the same. If you then also know resistance, you know current.