5. What does “seed proof” or “F1” mean on seed bags?

Seed-proof seeds = reproducible seeds
Propagation via seeds is only possible with solid seeds. Seeds of seed-resistant varieties pass on their characteristics to their offspring in a continuous inheritance stream. The variety characteristics do not change abruptly but gradually. Since non-seed varieties can be sown several times, they change or adapt to the location. This provides a good basis for further development of the crop and variety diversity.

F1 seeds = hybrid seeds
These varieties are “one-time” varieties. They cannot be propagated sensibly in private gardens. 
If a hybrid variety is further propagated, ONLY INFERTILE SEEDS will be formed or it will split into different forms. The variety as such is therefore NOT stable. Since hybrid varieties can only be sown once, they do not adapt to site conditions and do not change. (Source: Handbook of Seed Gardening/ A. Heistinger, Arche Noha, Pro Specie Rara).

It should be noted that cross-breeding could also occur with solid seeds (rare) if several varieties of the same plant family are next to each other. 

A very good graphic on the topic of seed-proof and hybrid seeds can be found at this link on page 20.