Your job is to act as a visual deterrent and you are doing that by simply turning up to work.
If the store has a serious problem with theft, they would have invested in CCTV, store detectives, etc. They havn't done this so surely it isn't that bad.. this just seems like one of those stores where the clueless managers think they know it all and try to do your job as well as there own. I think every supermarket has a few of these guys, they usually end up getting thrown through a window or punched in the face by an angry shoplifter every year
Acting as a visual deterrent doesn't mean just standing by the exit though, if you notice somebody suspicious enter the store or somebody acting suspiciously in store, you can go to the same aisle as them or you can stand at the top of the aisle that they are in. You don't have to be obvious about watching them but as long as you can see what they are doing, it's alright, if it's not possible to discreetly catch them at it, you can just make them aware that you are there and watching, so it deters them. There's only so much you can do in a store like this.
I sometimes used to talk to staff so customers would see me chatting away and think i was not on the ball. While i was talking to the staff members (usually somebody stacking shelves), they whole time i was actually looking at customers and seeing how they reacted to me, some people would see me and see that i was having a nice little chat and immediately turn around and go into another aisle to try there luck.. i did this in a store with CCTV so the manager could watch on the CCTV at the same time. This helped me catch a lot of the middle class shoplifters who would come in every week to do there weekly shopping and conceal a bit of make up or chocolates, something small but a bit pricey and you would never have suspected them. These people used to steal every single week and not get caught for years, but how they react around you and the way they are always looking around always gives them away. The managers were surprised because i caught loads by doing this and most of them had been shopping in the stores for years, they were always friendly and spoke to the staff every time they were in store, nobody would have suspected them at all.
Not much you can do about the trolley push outs apart from stop and ask for a receipt if you're unsure whether they paid or not, there's nothing wrong with that as long as you're polite. If they start to question why you're stopping them in particular, just say that you have been asked to do random stop checks on customers leaving the store. (make sure you check the time/date on the receipt, the Eastern European's in particular like to flash an old receipt at you but if you look closely, it's usually dated 6 weeks ago
Were the people who attempted push outs banned for attempted theft or did you just recover goods and let them go?? not sure on how it works in your store but i would ban them for trying that, an offense has been committed but because you have no CCTV, i would try to make a staff member aware of it just before it happens so it's not just your word against there's. If not, a member of public would do, somebody is bound to see what's going on and see you stop somebody, just ask them to wait at the side while you deal with it and take there details, just in case you need a witness (very unlikely but just to cover yourself because of no CCTV/proof)