1) I can't improvise a great melody: usually when I'm playing I'll play certain notes on the scale and then sometime decide " ...... But I don't remember the melodies I play earlier and can't recall them or reproduce them exactly.
With the level of experience you've described it's not surprising you can't improvise a great melody! It takes a while to learn how to do that, just as you've learned over time to play the piano.
It's hard to say without hearing you play but if you can't remember what you played earlier then it sounds like you're not "hearing" what you played earlier. "Hearing" meaning having some internal sense of what you've played.
A possible place to begin is FIRST hear what you'd like to play and then SECOND play what you hear. Of course no one hears EVERYTHING they play in advance and improvising is at times going to consist sometimes of FIRST playing something and SECOND hearing it. Because learning how to play what you hear is a skill. It takes time to acquire it and the learning process isn't straightforward.
The more you can do in the way of advance hearing the better off you'll be in terms of knowing how to begin and then how to continue. Knowing how to continue means understanding how to build an arc that takes you and your listener from point A to point B. It''s ironic and it can seem counterintuitive but the arc that goes from A to B–the music you're trying to improvise that tells a story–doesn't require a lot, if any, knowledge of chords or scales or theory. But it does require a willingness to work from what whatever it is you're hearing internally.
Here's an interview on my blog with Joey Alexanderhttp://www.polishookstudio.com/2014/02/interview-with-joey-alexander.html
He's an 11-year old pianist from Indonesia who's completely self-taught as an improviser. Herbie Hancock, among others has been mentoring him. Last I heard (from news reports) he was in NYC playing in jazz clubs and (with the supervision of his dad!!!!!) figuring out how to stay in NYC so he could grow there as a musician. But in any case, in the interview JA has advise for aspiring improvisers. It really is as simple as "tell a story .... if you don't have a story then make it up!
Whatever an idea might be for an improviser it usually takes a lot of experience to spin them out, much less effortlessly. Because you've said you have no real experience as an improviser it's perfectly natural that you run out of ideas. In fact if you have any ideas at all then you're doing great and you're way ahead of most beginning improvisers. As you acquire improvising experience your ideas will flow with more ease.
It may or may not apply directly to you - but it is often the case that pianists who have never improvised underestimate how much work goes into the profiency great improvisers demonstrate. That proficiency, among other things, can make improvisation seem to be easy. Well, it is easy with enough experience and study and practice. But, the experience and the work precedes the skill. That means trial and error and experimenting and practicing.
Do you have any ideas on how I can take this further and improve in the area of improvisation? Things like what chord progressions to use (because usually I can't do anything without a basic 'structure' to follow) or things to incorporate to make my improvisations more interesting? or how I can improve in general?
The question about where to begin is of course the first step! You could seek out some basic chord progressions. Or find "things to make your improvisations more interesting. But how much that'll help is debatable. A better place to start is with repertoire and sound–repertoire perhaps from a fake book and the sound of great improvisers from recordings, Youtube, etc. or live if possible.
I'm recommending sound as the important step because if you have a sense of the what the music you'd like to play sounds like then it becomes much easier to play it. Because we've brought the ear into the process. And music is about ears and hearing.
Something else to mention is that no matter where you are along the path (beginner, intermediate, advanced, world-class) a perfectly sound approach is: Improvise with the skill and technique you have now instead of with the skill and technique you wish you had and which you might have later. To improvise with the skill and technique you have now may mean you're improvisations are going to be simple and not all that ambitious. Perhaps. The idea is to bring things to the level at which you're actually hearing them.
I book I often recommend is The Primacy of the Ear by Ran Blake. Ran is one of the most influential teachers of improvisation anywhere worldwide. He's been teaching at the New England Conservatory in Boston for 30 or 40 years. Probably more like 40 years. The book describes an approach to improvising that, as the title suggests, is about the ear and hearing what you play. It has practical exercises and, really, every aspiring improviser should read it.
The short version of all above is do some listening. Find recordings of great improvisers who inspire you. Get the sound in your head. Read Ran Blake's book and get a better sense of how improvisation, the ear, and inner hearing are connected. Begin to improvise by listening to what you play. And playing no more than you can really hear. Get a fake book (of your choice) and learn melodies and do the best you can do with the chords. Remain non-judgemental throughout: play what you hear without worrying too much about whether it's good or bad or a variation on either. And pick up some theory along the way. But let theory build onto what you play. Instead of playing according to theory.
I hope this helps!