My question- is operating my bitcoin wallet using a wireless modem safe for my cash? For example- lets say that somebody uses internet offer from the same GSM operator, and is like using it few hundred meters from me. Isnt he going to have the same IP address and if yes- isnt my privacy and safety of my bitcoins in trouble?
Two users cannot have the same IP address simultaneously, though if someone connects to the network after you disconnect, they may be given your old IP address. Note that this applies equally to both wired and wireless networks.
Bitcoins are not sent to IP addresses*. Bitcoins are sent to Bitcoin addresses, which represent a cryptographic key. Only someone with the private key to that address (which is stored on the owner's computer and is never transmitted anywhere) can create a transaction to spend those coins. Bitcoin transactions are cryptographically signed to make modification or forgery impossible.
Privacy, however, may be an problem if others can monitor your Internet connection. Bitcoin-Qt can be run over Tor to avoid this issue, however MultiBit cannot (as far as I am aware).
*There used to be a "pay to IP" feature, but this was removed long ago due to how ludicrously unsafe it is.
Second question- is it worth to invest in a wireless router, instead of using only wireless modem (my is going to be Huawei E3131 to be precise)? Is it going to increase my safety?
No, it will not affect your safety or privacy at all (unless, of course, your computer is connected to the router insecurely, eg, over open WiFi). A router will make it easier for you to connect multiple computers, but that's all.
