Hello experts!

I am considering going to Seoul for a week next month but it's still not finalized and thus have not started any itinerary planning. This will be my first visit.

1. Understand it's still summer next month - is this a turn off since the weather is more or less like Malaysia? What are the recommended activities in summer?
2. If i were to go, i'll be staying at Shilla Stay Gwanghwamun hotel. Anyone can advise if this hotel/area is recommended? In terms of convenience, safety, proximity to train stations etc..
3. Roughly how much should i allocate per day (including average meals, public transportations, cafes, local ground tours, sight seeings and entrance fees etc etc)? I know shopping is very subjective so let's leave that out in the budget planning and i'm also not considering far places like Jeju.
4. I only have a week there and i'll be alone during the day. Off the top of your head, can you guys let me know what are the places i should go and explore as a first timer? Apart from Song Joong Ki and Myeong-dong for shopping, i'm totally clueless about Seoul.

It's a bit rush so i haven't got the chance to go through the previous posts. Need the experts here to help out so i can quickly finalize my decision!

Thank you so much guys!