re: "implementation the application of", I wholehearted agree with you - more than likely if I got this in a document to proof-read I would make the change. But, contextually, this is a specific technical issue being discussed as therefore might warrant the nominalisation. If you google "implementation the application of" looking for that exact phrase you get over 48 million hits. Whilst a lot of these (no, I'm not going to check :) ) are improper use of nominalisations, I'd suggest that the idea of using this phrase is not that unusual.
Re: 'A plan to', I assumed this was title to the thesis/report/whatever it is. Once again, I'll admit to not analysing the Polish request for what was actually needed in any great detail. In a business context 'we had a plan to' is a bit more convincing then simply 'we wanted to', as plan suggests structure, planning, organisation etc. But in other contexts I take your point.