Your issue looks to be with the battery under the bonnet. If your car runs fine without any hesitation or hard jerks when shifting gears (slight jerks can be felt, no worries there), then there is no issue with the gearbox - so please don't pay anyone to fix anything.
For the warning lights, just disconnect the battery under the bonnet for a minute or two, then reconnect it so that your ECU resets and the signs will go away. You may need to repeat this step one or two times. If they come back on, then your battery under the bonnet is most likely toast. However, to be on the safe side, get the battery checked from a reputable battery technician and if the battery is toast (which it most likely is) then replace it with a new one.
Regarding the ABS sensor wires, just look behind the wheel to find out where your ABS sensor and its wire is. Then follow that wire and check if it is loose or broken anywhere.
Last, if you recently bought the car, it might be a good idea to replace the fluids. For gear oil, use Honda DW1 fluid and for clutch fluid, use a DOT4 brake fluid from a reputed brand like Liqui Moly. This is to be done once your warning lights issue is fixed.
Let me know via PM if this solves your problem.