The thing with low carbing is that there are lot of different plans/ways to do it! And just cutting out refined carbs like bread/pasta/rice/potatoes and sugar is one way - so your diet so far is a lot better than it would have been before.
However, to comment specifically:
Breakfast: Greek yogurt full fat, nuts, a banana
The yoghurt is fine - and it should be full fat. If you're eating a low carb diet then it should be high fat and medium protein. However, the banana is a big no no - it's a really carby fruit
Snack: apple
Again, fruit isn't ideal - although apples aren't too bad, depending on what else you're eating during the day!
Lunch: 2 boiled eggs, 2 slices of ham, lettuce, cucumber, cherry tomatoes, baby corn, grapes
All good, apart from the grapes - they're high carb, and also more fruit. I hope that you also had mayo and/or an oily dressing on the salad?
Snack: carrot raw
Carrot is relatively high in carbs - and you've had two carby snacks in your day. What you should find after a few days of eating low carb is that you won't be hungry between meals, and so won't need to snack any more
Dinner: roast chicken, parsnips, broccoli
Parsnips are definitely out - they're very carby