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The seatbelt light not going out with the belt buckled is likely because of a bad switch in the buckle.
The brake warning lamp could be coming on due to an issue with the emergency brake switch circuit, whether wiring, the switch itself or the brake is moving just enough to allow the switch to close somehow, but since the light comes on under acceleration and goes off during deceleration it seems most likely that it's coming on due to low fluid level. There is a switch in the master cylinder reservoir that opens and closes depending on fluid level and will turn the red brake warning light on when the fluid level is low. Your fluid may be low enough either from a leak or from normal pad wear so that it's now at the level where it's just low enough to turn the warning lamp on intermittently.