That type of suspension is just an undamped spring; you can adjust the spring tension making it stiffer but as far as I know, locking it altogether is not possible unless by means of tightening the adjusting nut right up to the point where the spring is fully compressed - but that would drop the bottom bracket perhaps too far resulting in pedal strike. It would be better to remove all the bits and replace by a solid thing, such as taking out the spring and replacing it with an aluminium cylinder.

The brake levers could in principle be on bar-ends, if these were 22.2mm diameter. The brake cables would stick out a bit awkwardly perhaps.