Sympathies that you are struggling with the bronchiectasis aspects of your condition. I detect from viewing postings on this forum that those with a combination of COPD and bronchiectasis can have a tougher time than those like me with bronciectasis alone. But do put in some time to research further on this forum for ways of getting the best out of your bronchiectasis performance and it should help to improve your overall health.
The basics of any plan for bronchiectasis treatment would be:
* getting the best/consistent sleep that you can
* eating healthily in terms of volume and type of food; lots of fruit & veg; experiment with the stuff that others recommend (eg cider vinegar+honey for gut health, cutting out or down on dairy if sputum thickness is a problem)
*avoiding smoking - direct and passive
*getting weight under control - bronchX can increase the impact of any heart imperfections, so get the cholesterol and blood pressure under control
*daily exercise that increases your heart rate (don't be afraid to get out of breath is what my pumonologist said); the more the better
*daily sputum clearance excercises; there are leaflets that explain basic physio but at its simplest just lying on your back and/or side and inhaling deeply to 'huff' up and spit out the sputum (with periods of quiet breathing in between) is the basic approach; view postings of others to get other tips
*if your mucus is very thick or difficult to dislodge consider acquiring aids (acapellas, vibrating vests). Lots of discussion on these in this forum
*medications to improve:
-sputum clearance - many seem to benefit from mucolytics like carbocysteine and they seem to be low impact to most in terms of side effects
-breathing/keeping the airways open; steroids and bronchodilators in the form of inhalers or tablets
-antibiotics, either prophylactically to limit the potential for infection or to treat the onset of infection
A few other thoughts to adress your specific questions:
*I agree that GPs (in the UK, but probably worldwide) are not experienced enough to provide proper care. We should not be too hard on them. This disease is not common. Monitoring/advice by a pulmonologist is essential
*Prednisolone is a steroid which is an anti-inflammatory. If your doctor or pulmonologist or you thinks that inflammation is an issue for you (as it is either periodically or generally for most bronchiectasis sufferers) then it may well form part of your treatment; most of us have taken prednisolone at one time or another; the issue is that steroids have longer term side effects so they need to be treated with care. Inhaled steriods seem to be less problematic and are ok for short bursts of use, but I was slightly concerned by the implication of your posting that your GP had prescribed short bursts of prednisolone. As far as I know prednisolone takes some time to build up to be effective and I do know that they should not be stopped immediately, they need to be wound down with a stepped reducing dose
*There is no such thing as a "usual course of antibiotics" in terms of which antibi or length of treatment. 7 days is the minimum a UK doctor would prescribe an antibi for (any less is dodgy in terms of promoting resistance for your bugs to that antibi and those resistant bugs can then get out into the environment and prmote a potentially nation-wide and even world-wide resistance of a specific bacteria to that bug). It may not be sufficient to treat your condition and my experience is similar to another poster - I generally find 10 or 14 days are needed before I am confident that my infection is on the way out. If you press your GP for a longer course she/he will probably say "come back for more if the 7 days dosen't clear it". They have financial restrictions within the NHS. A pulmonologist would generally prescribe a longer dose
*Most (all?) bronciectasis sufferers have mucus on their lungs. It's stickiness is variable, so is its thickness, so is the ease with which it is coughed up. My own mucus is normally medium and comes up quite easily - both during the course of the day (as throat clearances without any coughing, or triggered as an impromptu cough or as response to active physio huff coughing). I take a daily mucolytic but I could probably get by without it - ie it helps marginally and gives me no issues.
*Many bronchiectasis sufferers get positive readings from their infected sputum which aids in using a targeted antibiotic. A few ('uncommon but not rare' per my pulmonologist) always get no specific bacteria identified results. Join the club - I am also one of those. When my infections were a bit more invasive, a year ago plus, my pulmonologist suggested that a broncoscopy might be useful to see if I had any particular strains. I see her again next month and would resist a procedure that is not guaranteed to find anything and slightly uncomfortable, given that my infections are now relatively infrequent (3 in the last year and only one was uncomfortable/lasting (more than a week).
* Having tried, under direction and then under my own self-prescription, various antibiotics over the 4 years of my diagnosed bronchiectasis, some of which worked well for a time and some hardly at all, I am now on a prophylactic dose 3 times a week of azithromycin. If I get an infection I step it up to the regular daily dose. The one time that did not kill the infection another pulmonologist recommended stepping back down to the prophylactic dose of azith and adding a full daily dose of Levafloxacin (which has worked well for me on pneumonia in the past); that worked within a matter of days.
*Azithromycin taken prophylactically is I think becoming the drug of choice for many bronciectasis sufferers who would otherwise get frequent or long-lasting infections. I observe that 4 out of 5 of those on this forum who mention azith report very positively on it. You should not immediately jump on it though - other less strong (and cheaper - for which reason NHS GPs may not readily prescribe it!) antibis may work just as well and taking prophylactic antibis can poduce longer term gut problems (though I have not experienced any).
*A poster raised the issue of not taking a particular antibi for fear of "running out" of antibis. While it is certainly sensible to start at the bottom and work your way though the range as slowly as you can tolerate let's not get too overboard on the "help, there's nothing left theory". If you 'run out' of tablet options then taking them in nebulised or intravenous form will probably be effective. If not there are specialised intravenous antibis taht we don't generally see. I have not yet seen a posting form someone reporting that they have exhausted all options. Still, as said, it is sensible to be cautious about switching up too quickly.
I've said enough. By all means ask more detailed questions if it helps