No, you're closer than it feels. Here are what they mean in more every day terms.)
Reflection symmetry - the laws of physics should be the same for an observer who is a mirror image of ourselves. (In classical mechanics this is so. In quantum mechanics you also have to reverse the sign of all charges.)
Translation symmetry - The laws of physics should be the same for an observer in a different position in space. (This one is true.)
Rotational symmetry - the laws of physics should be the same for an observer who is rotated from ourselves. (Again true.)
Combinations - just refers to combining things by some rule. A linear combination of vectors is just adding scalars times vectors. So the set of linear combinations of 2 vectors is the plane spanned by those vectors. A convex combination of points is any average of them. So the convex combinations of 3 points is a triangle. And if you allow some set of algebraic operations, from a fixed set of values you can generate a whole system. Those fixed values are generators for that system. So, for example, (1, 0) and (0, 1) with the algebraic operations of addition and subtraction generate the whole grid of points (n, m) with n, m integers. In all of these cases you can often work with just the few things from which the plane/triangle/grid/whatever was created, without having to look at the rest.
Dense subclass - for any point you choose, for any distance you choose, the dense subclass includes something at least that close. For example the rational numbers are dense within the reals. Pi is not a rational number, but we have no trouble finding rational numbers within 1 billionth of pi. So you can sometimes prove something for all rational numbers, and then find you've proven it for all real ones. (For example, with powers, roots, and division we can define 2^x for all rational numbers x and prove properties about it. From that we can actually define 2^x for all real numbers.)
Reflection symmetry - the laws of physics should be the same for an observer who is a mirror image of ourselves. (In classical mechanics this is so. In quantum mechanics you also have to reverse the sign of all charges.)
Translation symmetry - The laws of physics should be the same for an observer in a different position in space. (This one is true.)
Rotational symmetry - the laws of physics should be the same for an observer who is rotated from ourselves. (Again true.)
Combinations - just refers to combining things by some rule. A linear combination of vectors is just adding scalars times vectors. So the set of linear combinations of 2 vectors is the plane spanned by those vectors. A convex combination of points is any average of them. So the convex combinations of 3 points is a triangle. And if you allow some set of algebraic operations, from a fixed set of values you can generate a whole system. Those fixed values are generators for that system. So, for example, (1, 0) and (0, 1) with the algebraic operations of addition and subtraction generate the whole grid of points (n, m) with n, m integers. In all of these cases you can often work with just the few things from which the plane/triangle/grid/whatever was created, without having to look at the rest.
Tensors - not going through that topic here. Start with https://en.wikipedia.org/wiki/Tensor_product if you're curious.
Dense subclass - for any point you choose, for any distance you choose, the dense subclass includes something at least that close. For example the rational numbers are dense within the reals. Pi is not a rational number, but we have no trouble finding rational numbers within 1 billionth of pi. So you can sometimes prove something for all rational numbers, and then find you've proven it for all real ones. (For example, with powers, roots, and division we can define 2^x for all rational numbers x and prove properties about it. From that we can actually define 2^x for all real numbers.)