There were rumours about the restaurants McDonald's cooking their fries in beef lard/oil if I remember correctly but apparently they stopped that a few years back. However some people still say it's best not to eat their food as they could still be doing so or even just using the same utensils for vegetarian foods which we can eat and for haram foods too.

Also a lot of other restaurants such as domino's pizza, subway, nandos and a lot of other takeaways – they have halal options, vegetarian options and also haram options. Can we still buy and eat from their food or should we avoid due to the possibility of cross contamination and foods being cooked in the same oven for example?

It’s your responsibility to find out from your local restaurant to ascertain what is been speculated. Each restaurant differ depending on the locality. Kindly find out by either asking the management or people you trust.