To England with Italian passport

Is it possible to get into England without an end date? (I will look for a job and stay there if I can, maybe one or two years.)

Yes. As an Italian citizen, you enjoy freedom of movement in the entire EU, which allows you to move to the UK indefinitely. After the UK leaves the EU, those EU citizens who arrived before a certain date will be able to remain in the UK, but the details (and the certain date) are not yet fixed.

Do you need something else besides the passport?

To stay for up to three months, no. After three months, you can be required to show that you are "qualified" under the freedom of movement law. This essentially means that you are either employed, looking for work (under certain circumstances), studying, or self-sufficient. In the last two cases, you also need "comprehensive sickness insurance." But for the initial entry, as for the first three months, you do not need any of that.

I am quite scared for different checks in the border.

For an EU citizen, the checks are quite minimal. Because you can easily qualify for a right to stay indefinitely, the checks are mostly limited to establishing that your passport is genuine and valid, and that it belongs to you.

The June 16, 2011 consolidated version (the most recent as of this writing) of the EU freedom of movement directive, 2004/38/EC, is available from eur-lex.

The UK law that implements the directive is available (currently with a disclaimer that cautions that there are changes that have not yet been incorporated into the revised version) at The Immigration (European Economic Area) Regulations 2016.

The relevant parts of the UK regulations for your question are:

11.—(1) An EEA national must be admitted to the United Kingdom on arrival if the EEA national produces a valid national identity card or passport issued by an EEA State.

and

13.—(1) An EEA national is entitled to reside in the United Kingdom for a period not exceeding three months beginning on the date of admission to the United Kingdom provided the EEA national holds a valid national identity card or passport issued by an EEA State.

(See also 13(3) which provides that those who are an "unreasonable burden on the social assistance system of the United Kingdom" lose the right to reside.)

14.—(1) A qualified person is entitled to reside in the United Kingdom for as long as that person remains a qualified person.

Finally, the definition of qualified person is at regulation 6, and is too long to be quoted here in its entirety, but it implements the directive's Article 7(1):

Article 7

Right of residence for more than three months

1. All Union citizens shall have the right of residence on the territory of another Member State for a period of longer than three months if they:

   (a) are workers or self-employed persons in the host Member State; or

   (b) have sufficient resources for themselves and their family members not to become a burden on the social assistance system of the host Member State during their period of residence and have comprehensive sickness insurance cover in the host Member State; or

   (c)
   — are enrolled at a private or public establishment, accredited or financed by the host Member State on the basis of its legislation or administrative practice, for the principal purpose of following a course of study, including vocational training; and
   — have comprehensive sickness insurance cover in the host Member State and assure the relevant national authority, by means of a declaration or by such equivalent means as they may choose, that they have sufficient resources for themselves and their family members not to become a burden on the social assistance system of the host Member State during their period of residence; or

   (d) are family members accompanying or joining a Union citizen who satisfies the conditions referred to in points (a), (b) or (c).