Potter here. Those cracks are very bad, and are the kind that will continue to spread each time the teapot heats and cools; I doubt you have too many uses before it falls apart entirely. You should consider whether it's worth trying to salvage that teapot at all. Assuming you want to, though, I'll outline the methods.
Those cracks, by themselves, are not a food safety issue. Tea is fairly antiseptic, and just having some in the cracks doesn't really expose you to anything. It's pretty common to make teapots out of porous earthenware because nobody is worried about bacteria in tea.
You have three ways to seal those cracks: epoxy, silicone, and milk.
Epoxy: various food-safe epoxies can be used to fill in the broken areas. This will make your strongest and most durable bond, and will fill that divot nicely. However, it's going to be difficult to seal the hairline cracks, because there's no way to get the epoxy into the crack. You could consider cracking the teapot the rest of the way, and then epoxying the whole thing back together. Some people even do this with decorative elements in a technique known as kintsugi.
Silicone: there are also various food-safe silicone sealants. While these do not have as much binding strength as epoxy, they will fill that divot well, and possibly work better for smearing on the hairline cracks to seal them. You can also use a dilute silicone sealant to try to coat the inside of the pot. However, such sealants don't bind well to glazed surfaces, and may affect the flavor of the tea.
Milk: the casein in cow's milk has been used as a sealant for earthenware pottery, and for crazed glazes. While this won't bind the crack (you'll still need epoxy for that), it's obviously a cheap and easy way to seal the inside. However, the sealing ability of milk is disputed, and the milk technique is not generally used for vessels that will hold hot liquids.