Tomatoes contain citric acid (they're actually classed as a fruit) and this can take some people out of ketosis.
Yes, you can eat swede on sns. My latest veg list gives:
200g of: asparagus, bamboo shoots (canned, drained), broccoli, cauliflower, celery, courgettes, cucumber, fennel, gherkins, green peppers, green chilli peppers, leeks, lettuce, mushrooms (not fried), olives, rocket, salad, shallots, spinach, spring onions, swede (flesh only), turnip (flesh only and must be boiled), watercress, white cabbage.
There's other information in the SnS sections here on the veggies allowed - put some keywords into the search box at the top of the page and see what you get!