The BBC has already been listed but can I also suggest the comment/blog pages on the Telegraph (the leading relatively high-brow right wing/conservative paper) and the Guardian (the leading left wing/progressive paper) for differing views on what the key issues of the day are. The Sun is the most popular paper and so looking at that gives an idea of what the "man on the street" considers the biggest stories.
Going onto detail on each of the issues you pose.
Hot topics of the day (government scandals, etc)
The biggest domestic topic right now are the government cuts as a result of the recession. You could write a couple of thousand pages on the ins-and-outs of it all but the simple facts are there are going to be pretty big cuts that will effect a lot of people, some tax rises, the unions are rattling their sabres, the disabled are being dealt a very (very) bad hand and students have already staged some protests about the increase in tuition fees.
Recent conflicts in England and the role of the US in those conflicts
I'm not sure quite what is meant by conflicts in England which makes it hard to answer the question... and what conflicts we have had within the UK don't really involve the US. In terms of conflicts involving the UK, there's obviously Iraq and Afghanistan where the general opinion is that both were bad and that Blair (our former Prime Minister) acted as little more than a lapdog to George Bush in those conflicts. There's also a certain resentment large to a number of friendly fire incidents that occurred during the wars although at this stage it's normally relegated to jokes. In certain areas you'll find some pretty serious resentment of the US for their current policy on the Falkland Islands but it's not a mainstream issue by any means.
US role in local economy, politics, culture, etc.
The US is of course vitally important to the UK economy. The US is our single biggest export market and one of our most profitable, our financial institutions and supporting industries work closely with the US to the extent they are almost indistinguishable (which means the US doesn't take much blame for the financial crisis) and many US companies invest in the UK and employ large numbers. There's a certain resentment that things seen as "English" industries have been bought by American companies and somewhat asset stripped... the most notable being Cadbury's (a household name confectionery brand) being bought by Kraft with promises that a factory would remain open only for it to be almost immediately closed.
With regards to politics there's still a slight ill feeling that we're subservient to the US although that was mainly associated with Blair following George Bush into Iraq. Again, within certain communities there's some resentment to what's seen as the UK doing what the US says still... the arrest of Julian Assange was seen as Sweden and the UK doing the US's work, the case of the hacker Gary McKinnon and the extradition treaty that relates to that case etc etc, but those aren't big issues the general public puts much worry into. Politics in the UK has been dominated for the last two years or so by an expenses scandal that involved almost every MP, the general election and the recession and so there hasn't been much emphasis on the US influence.
There's a general disdain for what's seen as the "Americanisation" of culture but it's somewhat false. People will object to it... while happily grabbing a meal at McDonald's, listening to Lady Gaga, going to the cinema to see Generic Hollywood Blockbuster No.4 and watching Friends. Considering the absolute dross that makes up the vast majority of the UK's drama output (with some notable exceptions) imports like the Soprano's, The Wire or Mad Men are seen as a blessing... to the extent there's been a major new channel launched basically just showing those type of shows. That said other things that may be considered staples of US culture are basically unknown in the UK.
Types of gifts appropriate to bring new friends or host family (if applicable)
There's no formalised thing as to where/when you should bring a present. For a host family flowers, chocolates, a cake, a decent bottle of wine... basically depending on them and what you consider appropriate. As for gifts for new friends... it's not exactly a common occurrence. Offering to buy someone a drink down the pub/bar/coffee shop is pretty universal but outside of that it's very dependant on circumstances.
On the sports team's side of things the biggest sport is football (soccer). The most supported/famous/successful teams are Manchester United, Chelsea, Liverpool and Arsenal. Basically it breaks down sort of like this: Man United are the most famous, most successful over the past decade and most generally disliked although they also probably have the most "casual" fans, Chelsea were bought a few years back by a Russian billionaire who poured money in and basically bought them a team of superstars which led to some resentment but that's been superseded by other teams who have attempted to buy the title, Arsenal play the most attractive football but are seen as arrogant and Liverpool have the most tradition but are seen as delusional about their current status.
As Oniya says teams are fairly localised... you're unlikely to find huge numbers of Blackburn fans living in say West Ham... but at the same time you'll generally find people who support one of the big teams everywhere in the UK.
The only other team sport to have large scale support is Rugby... Union in the south of England and League in the North... with Union being more popular overall. There's actually a Rugby thread on here a little bit down running through certain teams... the most casually popular is probably Leicester but none of the teams have support on a level even close to football. Cricket is fairly popular, especially in the home counties, but people are far more likely to support the sport itself rather than an individual county team,.