Skip patterns in surveys relate to whether a value should be there or not.
One simple example If a person is female you do not ask them male specific health questions, or you only ask questions about certain topics if the response to question is a specified answer, such as person that says yes to a question like "have you ever been diagnosed with diabetes" gets additional diabetes management related questions but someone that answers No would not have answers to those questions.
So to make the time for the interviewer and respondent quicker the questions are not asked at all, i.e "skipped". Which results typically in missing data based on the order and requirements in the survey.
I am not reading the entire website but I am going to guess that the (box 2) after the response categories is a note about which group of questions get asked next when that response is chosen.
Your specific question: BPQ020 is "Have you ever been diagnosed with high bloodpressure"(to paraphrase). If you answer this "NO" why would need to know BPQ030 "were you told 2 or more times"?
The "recoding" depends on what you intend to do with variables. You might want to insert a value for the missing variables that indicate "intentionally skipped" or remove the "don't know" and "refused" categories so you can more easily get the percentage of Yes/No responses among the respondents that answered one of those two categories.
Other recode approaches might reduce the number of categories because you had many choices, such as a 1 to 100 scale but the individual responses didn't provide much information but grouping the responses to "low" , "middle" and "high" with some rule might more easily show something of interest.
Another reason for recoding is providing and answer choice of "other" with a follow up to collect a description of what the respondent means by "other". Some times you can code that "other" back to a response category. One of the surveys I worked with asked question about what race the respondent identified as with response choices like "white", "black", "american indian", "asian" plus "other" and were asked what the meant by other. I have coded literally dozens of responses that were "white" and "black" entered in the "other" response.
