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The behaviour you want is the default, so it seems you’ve got something set wrong.

If you’ve set a date under Default calendar start date (optional) then it will always start from that date. Clear the date in there and you should restore the behaviour of using the current date.

The easiest way to remove the categories selector is to hide it using CSS that you’ll need to add to your site (eg: using a plugin or the WP theme for your site). The CSS you want will depend on if you’re also using tags or not.

If you’re not using tags, try:

.ai1ec-calendar-toolbar {display:none}

If you’re using tags, or have some other content that appears in the toolbar that you want to keep, try:

.ai1ec-category-filter {display:none}

Also, if you want to hide tags but keep categories, try:

.ai1ec-tag-filter {display:none}

Note: You may need to replace the none with none !important in the above CSS in some cases. I found this to be the case with the category & tag filters on my site, but not for the toolbar. YMMV.

Sounds like a timezone issue.

Check the timezone of the calendar you’re importing from, and also check the timezone set in WordPress ( Dashboard->Settings->General ) AND in Ai1ec ( Dashboard->Events->Settings–>Viewing Events ). If they are different, you will get a difference.

In Ai1ec, you might also try the setting Display events in calendar time zone at the bottom of the Viewing Events tab, and then checking the details page for the event to see what it thinks the timezone is.

Something of note that I found through testing:

The plugin is really slow if your host is using php 5.4 or below, whereas if you’re using php 5.6+ it doesn’t seem to have any of these issues.

I suspect this is mainly due to the new Zend Opcache code that is present in php 5.6 and up.

FWIW: Rough values for a site I tried it on were:
6.5-7 secs without bwp (php 5.4)
30+ secs with bwp (php 5.4)
5.5-6 secs without bwp (php 5.6)
4.5-5 secs with bwp (php 5.6)

1. All the navigation options can be hidden using CSS (almost everything has it’s own CSS tag). You will need a way to add CSS to your site (eg: via your WP theme or a plugin) to be able to customise this behaviour.

2. Some of these are available via shortcodes. Look at “Shortcodes” under Events->Settings–>Advanced.

This isn’t an issue with the plugin per se, but depends entirely on iThemes security’s interpretation of what “Filter Suspicious Query Stings” means.

From brief exposure to this, it assumes that any query string that is passed to WP which is not a number or a common word is suspicious.

Ai1ec encodes a lot of data in URLs that fetch event information, and it’s usually these that iThemes Security marks as bad. It encodes this information to reduce the length of the URL being fetched.

Just to confirm here; it’s iThemes Security that is blocking you from accessing these URLs. I think you’d be better off trying to get iThemes to handle the issue so that their product handles such situations better, or includes an exception for what is obviously “known good” behavior that some plugins use.

Sounds like you’re using some sort of “Slider” plugin on your site that is incompatible with the plugin (looks like Rev Slider 2.4). I’d try disabling any slider plugins and see if the problem goes away to narrow it down.

You need to get your web host provider to increase the PHP memory limit for your website.

Note: The amount you currently have is listed in the error message. eg: allocated 34865152 = 33.25MB (divide by 1048576 to go from bytes to megabytes). You most likely need at least 64MB for a standard setup.