Well if you have installed mods with SAMI you should un-install those mods and your game should start to work fine.
If the above does not work,re-install GTA to fix this problem.
to me it looks like your GTA has problems loading textures which means that this is a client-side problem. This may be caused because of excessive use of mods in your GTA sa and re-installing your game will fix this problem. Your internet has no problems at all because you can still see all server items like house icons. If re-installing your copy of GTA does not work torrent another copy of GTA sa (I do not want to encourage torrenting or any other illegal downloads but as you bought gta, you should have the right to torrent that software because you have paid for it).
EDIT : There are also signs of lag, try closing some background processes that you do not need while playing GTA, if this does not work lower the GTA SA level of detail to low.
Press thanks if this helped you