SRQ Controller described multiple conflict events involving intersecting runways; same altitude assignments; and procedural errors on the part of the Local Controller.

Narrative

A Skyhawk [was] doing touch-and-go training on Runway 22. An Aerostar [was] landing on Runway 32. [There was an] apparent tie at mid-field intersection and the Controller issued the Skyhawk a go-around instruction. Skyhawk didn't respond; so Aerostar was issued the go-around; but not given instructions to turn. Result was Skyhawk in the midfield intersection and airborne while Aerostar passed overhead well above; but altitude above Skyhawk unknown. Same two aircraft transition the pattern with instructions to the Aerostar to climb to 1;500 FT for traffic (the Skyhawk). I coordinated the altitude with Approach Control. Skyhawk apparently took the Aerostar's altitude assignment; resulting in both aircraft being at 1;500 FT on converging courses; 2 [miles] east of the airport. I do not know if the aircraft had visual with each other; but they passed without incident. Next; the same Aerostar was landing Runway 32 and a C-182 Skylane was landing Runway 22. Another tie was apparent. Since the Skylane was just about to touch down; the Controller instructed the Aerostar to land Runway 32 and hold short of Runway 22. This procedure is not authorized for that particular runway configuration. I did not intervene and instruct the Controller to send the Aerostar around as it was in the best interest of safety to allow the operation to continue as issued. Both aircraft were on their respective runways at the same time. The Skylane ended up landing on Runway 22 and turning at an intersection well short of Runway 32. Recommendation; hear back/read back refresher; awareness training; scanning refresher; and intersecting runway operations training.