Can a tracheostomy make it difficult to eat?

Yes. Temporary swallowing dysfunction can be seen in patients with tracheostomy. Most facilities have a process to screen for this problem. Speech therapists are often consulted to assist with improved swallowing.
Yes. The trach tube with it's ties around the neck can keep the voicebox from bobbing up and down during swallowing and make it difficult to swallow normally. Most people get over this sensation over time. Make sure the trach ties are not too tight.